In this notebook, I will walk through solving a complete machine learning problem using hypothetical weather conditions inside a greenhouse dataset.
This is a supervised, regression machine learning task: given a set of data with targets (in this case the yield) included, we want to train a model that can learn to map the features (also known as the explanatory variables) to the target.
Supervised problem: we are given both the features and the target Regression problem: the target is a continous variable, in this case ranging from 0.38-1.07
The objective is to find a specific model for a greenhouse that can predict its yield with the accuracy of more than 92%.
Machine Learning Workflow¶
The structure of the machine learning project will be as follows:
- Data cleaning and formatting
- Exploratory data analysis
- Feature engineering and selection
- Establish a baseline and compare several machine learning models on performance metric (MAPE)
- Perform hyperparameter tuning on the best model to optimize it for the problem
- Evaluate the best model on the validation set and make prediction on the test set
- Interpret the model results to the extent possible
- Draw conclusions
Imports¶
I will use the standard data science and machine learning libraries: numpy, pandas, and scikit-learn. I also use matplotlib and seaborn for visualization.
In [422]:
# Pandas and numpy for data manipulation
import pandas as pd
import numpy as np
# No warnings about setting value on copy of slice
pd.options.mode.chained_assignment = None
# Display up to 60 columns of a dataframe
pd.set_option('display.max_columns', 60)
# Matplotlib visualization
import matplotlib.pyplot as plt
%matplotlib inline
# Set default font size
plt.rcParams['font.size'] = 24
# Internal ipython tool for setting figure size
from IPython.core.pylabtools import figsize
# Seaborn for visualization
import seaborn as sns
sns.set(font_scale = 2)
# Splitting data into training and testing
import random
from sklearn.model_selection import train_test_split
# Machine Learning Models
import lightgbm as lgb
from sklearn.linear_model import LinearRegression
from sklearn.ensemble import RandomForestRegressor, GradientBoostingRegressor
from sklearn.svm import SVR
from sklearn.neighbors import KNeighborsRegressor
# Hyperparameter tuning
from sklearn.model_selection import RandomizedSearchCV, GridSearchCV
# LIME for explaining predictions
import lime
import lime.lime_tabular
In [423]:
data = pd.read_csv('dataset.csv')
# Display top of dataframe
data.head()
Out[423]:
| week_num | yield | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | ... | 4311 | 4312 | 4313 | 4314 | 4315 | 4316 | 4317 | 4318 | 4319 | 4320 | 4321 | 4322 | 4323 | 4324 | 4325 | 4326 | 4327 | 4328 | 4329 | 4330 | 4331 | 4332 | 4333 | 4334 | 4335 | 4336 | 4337 | 4338 | 4339 | 4340 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Week 48 FY15 | 0.57 | 0.765056 | -0.356439 | 0.197052 | 0.795395 | 0 | -0.001015 | 0.196354 | 0.081835 | 0.950103 | -0.063364 | -0.829207 | -0.241069 | 1.456464 | -0.330876 | 0.018767 | 0.260456 | -0.067674 | 0.525733 | -0.131478 | -0.474496 | -0.229206 | -0.436584 | -0.391205 | -0.291944 | -0.394279 | 0.015729 | -0.661840 | -0.221699 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 1 | Week 49 FY15 | 0.47 | 1.062557 | -0.156156 | -0.234454 | 0.950919 | 0 | -0.170481 | -0.057973 | 0.362018 | 0.590900 | -0.030287 | -0.808753 | 0.520046 | -0.331018 | 1.098410 | -0.036730 | 1.044749 | -0.154249 | 0.656448 | -0.159455 | -0.758297 | -0.190549 | -0.332570 | 0.349147 | 0.341943 | -0.310972 | 0.303210 | -0.558677 | -0.133704 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 2 | Week 50 FY15 | 0.43 | 0.961968 | -0.276802 | 0.106828 | 1.075338 | 0 | -0.004001 | 0.110006 | 0.201414 | 0.516113 | -0.016122 | -0.772992 | 0.347968 | -0.331018 | 0.772261 | 0.225179 | 0.792992 | -0.104244 | 0.553572 | -0.175071 | -0.563206 | 0.008438 | -0.469626 | 0.413091 | 0.442866 | -0.420743 | 0.414846 | -0.595874 | -0.101545 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 3 | Week 51 FY15 | 0.49 | 0.864231 | -0.411954 | 0.174596 | 1.168652 | 0 | 0.040849 | 0.032461 | 0.311033 | 0.605321 | -0.023123 | -0.711317 | -0.098511 | -0.331018 | -0.485911 | -0.064177 | 0.610803 | -0.110098 | 0.553419 | -0.201746 | 0.084896 | -0.078933 | -0.542146 | 0.656361 | 0.552064 | -0.478825 | 0.474788 | -0.449464 | -0.085681 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 4 | Week 52 FY15 | 0.57 | -0.083462 | -0.212342 | 0.110023 | 1.251599 | 0 | 0.021135 | -0.133111 | 0.152851 | 0.944587 | 1.262242 | -0.840133 | 1.034012 | -0.331018 | 0.471113 | -0.287214 | 0.642511 | -0.140182 | 0.083886 | -0.212156 | -0.806272 | -0.432690 | -0.568484 | 0.453516 | 0.341360 | -0.499920 | 0.375777 | -0.458860 | -0.107713 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
5 rows × 4342 columns
Taking a look at the raw data, we can already see that the ranges of variables' values are not very different. Although all I know from the problem statement is that we want to predict the number in the yield column that has a masure unit kg/m2, and the rest of the varibles are just numbered, I can make an educated guess and say that the variables have been standardized/normalized due to different unit measures and value ranges.
Data Types and Missing Values¶
Further, I will take a look at the data types to make sure they make sense(have the coressponding data type assumed correct)
In [424]:
# See the column data types and non-missing values
data.info()
<class 'pandas.core.frame.DataFrame'> RangeIndex: 131 entries, 0 to 130 Columns: 4342 entries, week_num to 4340 dtypes: float64(4327), int64(14), object(1) memory usage: 4.3+ MB
Most of the variables seem to be numeric, except the week number column beeing object type (string). To be later checked why 14 variables are innt64 and not float type.
In [425]:
# Statistics for each column
data.describe()
Out[425]:
| yield | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | ... | 4311 | 4312 | 4313 | 4314 | 4315 | 4316 | 4317 | 4318 | 4319 | 4320 | 4321 | 4322 | 4323 | 4324 | 4325 | 4326 | 4327 | 4328 | 4329 | 4330 | 4331 | 4332 | 4333 | 4334 | 4335 | 4336 | 4337 | 4338 | 4339 | 4340 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 115.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.0 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | ... | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 |
| mean | 0.675391 | 0.012175 | -0.011646 | 0.032254 | 0.026639 | 0.0 | -0.061272 | -0.039280 | -0.022693 | 0.009954 | -0.006165 | 0.010942 | -0.093526 | -0.070380 | -0.006834 | -0.003581 | 0.007788 | 0.008028 | -0.003892 | -0.043079 | 0.019994 | 0.028660 | -0.019106 | 0.000588 | -0.000803 | -0.025285 | 0.000811 | -0.017509 | 0.005951 | 0.016551 | ... | 0.019847 | -0.018212 | 0.015140 | -0.012253 | 0.015139 | 0.013703 | -0.013526 | 0.015146 | 0.013796 | -0.017083 | 0.019840 | -0.013002 | 0.019632 | -0.017392 | 0.014745 | 0.015139 | -0.010341 | -0.023997 | 0.014198 | 0.014973 | 0.011159 | 0.015135 | -0.000732 | 0.011064 | 0.001800 | 0.015146 | -0.016099 | 0.014991 | -0.016266 | -0.018191 |
| std | 0.173095 | 0.992832 | 0.998961 | 0.974747 | 0.987683 | 0.0 | 0.671533 | 0.938874 | 0.968220 | 1.000330 | 1.008214 | 1.007417 | 0.574728 | 0.820738 | 1.009729 | 1.010899 | 1.009461 | 1.009276 | 1.000959 | 0.940680 | 0.998142 | 0.945582 | 0.973479 | 1.010564 | 1.010149 | 0.953264 | 1.010806 | 0.983389 | 1.009957 | 1.002341 | ... | 0.998339 | 1.000419 | 1.003851 | 1.006448 | 1.003852 | 1.005233 | 1.005352 | 1.003845 | 1.005148 | 1.001739 | 0.998349 | 1.005716 | 0.998624 | 1.001403 | 1.004245 | 1.003852 | 1.007746 | 0.992102 | 1.004773 | 1.004018 | 1.007339 | 1.003856 | 1.006302 | 1.007410 | 1.009994 | 1.003845 | 1.002811 | 1.004001 | 1.002566 | 1.000447 |
| min | 0.380000 | -2.276594 | -0.600320 | -1.344745 | -1.765569 | 0.0 | -0.428650 | -7.752403 | -8.845893 | -3.391754 | -0.186073 | -0.885389 | -1.071456 | -0.331018 | -1.373330 | -5.433454 | -2.357776 | -0.415026 | -3.336172 | -0.240134 | -1.307903 | -7.622581 | -0.568484 | -10.386934 | -9.415406 | -0.499920 | -8.203347 | -0.739742 | -1.229447 | -1.150176 | ... | -1.300000 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.991360 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 25% | 0.525000 | -0.726656 | -0.445459 | -0.786582 | -0.733926 | 0.0 | -0.277096 | -0.212699 | -0.212299 | -0.212930 | -0.125539 | -0.753347 | -0.460810 | -0.331018 | -0.739639 | -0.160585 | -0.418765 | -0.286940 | -0.653723 | -0.220940 | -0.637095 | -0.097085 | -0.544300 | -0.175117 | -0.156850 | -0.474049 | -0.070744 | -0.549544 | -0.202120 | -0.805935 | ... | -1.300000 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.991360 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 50% | 0.650000 | 0.131757 | -0.351201 | -0.017179 | 0.162930 | 0.0 | -0.149212 | 0.104851 | -0.024938 | 0.185155 | -0.110266 | -0.408105 | -0.229996 | -0.331018 | -0.285495 | -0.025708 | 0.314754 | -0.104244 | 0.258382 | -0.201746 | -0.243295 | 0.129581 | -0.334035 | 0.083081 | 0.126280 | -0.310972 | 0.096966 | -0.317995 | -0.174289 | -0.164899 | ... | 0.588668 | 0.894109 | 0.936147 | 0.457846 | 0.862280 | -0.260324 | 0.470975 | 0.948911 | -0.703088 | 0.537219 | 0.617484 | -0.121098 | 0.582681 | -0.811748 | 0.492216 | 0.934064 | -0.752612 | 0.357856 | -0.353018 | 0.534925 | -0.730907 | 0.927847 | -0.178247 | -0.202833 | -0.333432 | 0.927506 | 0.839520 | 0.742849 | 0.401413 | -0.800299 |
| 75% | 0.820000 | 0.868233 | -0.249513 | 0.689194 | 0.930182 | 0.0 | 0.022078 | 0.409939 | 0.128273 | 0.416063 | -0.081012 | 0.559834 | 0.113267 | -0.331018 | 0.653403 | 0.160909 | 0.789570 | 0.104917 | 0.736178 | -0.179883 | 0.497446 | 0.415257 | 0.155760 | 0.368455 | 0.348405 | 0.045178 | 0.338238 | 0.054899 | -0.133377 | 0.484090 | ... | 0.842512 | 0.941332 | 0.990198 | 1.010513 | 1.013364 | 0.861445 | 1.009165 | 1.001910 | 1.148301 | 0.961256 | 0.861348 | 1.022361 | 0.879483 | 1.184753 | 0.932457 | 0.986209 | 0.903354 | 0.870551 | 0.958373 | 1.049698 | 1.022801 | 0.985124 | 0.253157 | 0.328903 | 0.009021 | 1.000359 | 0.960832 | 0.950500 | 0.838910 | 1.095020 |
| max | 1.070000 | 1.711989 | 2.985258 | 2.743958 | 1.251599 | 0.0 | 7.262550 | 1.142294 | 3.174728 | 7.053521 | 11.358507 | 3.373740 | 3.117461 | 4.307555 | 2.872462 | 6.954217 | 1.312071 | 11.140575 | 2.087265 | 7.907794 | 3.220929 | 0.873747 | 4.481160 | 1.102200 | 1.056587 | 4.234904 | 0.828886 | 3.591991 | 7.193852 | 3.744339 | ... | 0.995714 | 1.200532 | 1.182414 | 1.316671 | 1.102186 | 2.091451 | 1.323212 | 1.125495 | 1.559355 | 1.204925 | 0.968651 | 1.527287 | 1.077952 | 1.405106 | 1.871936 | 1.188678 | 2.651805 | 1.949017 | 1.764962 | 1.386134 | 1.936779 | 1.223061 | 2.690308 | 3.203145 | 3.669438 | 1.187765 | 1.114567 | 1.424802 | 1.683484 | 1.713457 |
8 rows × 4341 columns
Missing Values¶
Now that we have the correct column datatypes, we can start analysis by looking at the percentage of missing values in each column.
Following is a function that calculates the number of missing values and the percentage of the total values that are missing for each column.
In [426]:
# Function to calculate missing values by column
def missing_values_table(df):
# Total missing values
mis_val = df.isnull().sum()
# Percentage of missing values
mis_val_percent = 100 * df.isnull().sum() / len(df)
# Make a table with the results
mis_val_table = pd.concat([mis_val, mis_val_percent], axis=1)
# Rename the columns
mis_val_table_ren_columns = mis_val_table.rename(
columns = {0 : 'Missing Values', 1 : '% of Total Values'})
# Sort the table by percentage of missing descending
mis_val_table_ren_columns = mis_val_table_ren_columns[
mis_val_table_ren_columns.iloc[:,1] != 0].sort_values(
'% of Total Values', ascending=False).round(1)
# Print some summary information
print ("Your selected dataframe has " + str(df.shape[1]) + " columns.\n"
"There are " + str(mis_val_table_ren_columns.shape[0]) +
" columns that have missing values.")
# Return the dataframe with missing information
return mis_val_table_ren_columns
In [427]:
missing_values_table(data)
Your selected dataframe has 4342 columns. There are 1 columns that have missing values.
Out[427]:
| Missing Values | % of Total Values | |
|---|---|---|
| yield | 16 | 12.2 |
Although we want to be careful to not discard information and should be careful when dropping columns, if a column has a high percentage of missing values, then it probably will not be of much use.
What columns to retain may be a little arbitrary here is a discussion, but for this project, if has been the case- I would have removed any columns with more than 50% missing values.
Here the only missing values are those in yield column, which correspond to the future trainig test split, so is as it is intentionally.
In [428]:
# Get the columns with > 50% missing (generic)
missing_df = missing_values_table(data);
missing_columns = list(missing_df[missing_df['% of Total Values'] > 50].index)
print('We will remove %d columns.' % len(missing_columns))
Your selected dataframe has 4342 columns. There are 1 columns that have missing values. We will remove 0 columns.
In [429]:
#Select the int64 type variables for inspection
data.select_dtypes(include=['int64']).head(10)
Out[429]:
| 5 | 315 | 625 | 935 | 1245 | 1555 | 1865 | 2175 | 2485 | 2795 | 3105 | 3415 | 3725 | 4035 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 2 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 4 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 5 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 6 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 7 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 8 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 9 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
It seems that these variables have constant value of zero, hence the int64 data type. Not sure if it's normal, as I am not aware of the columns significance.
Removing Outliers¶
When we remove outliers, we want to be careful that we are not throwing away measurements just because they look strange. They may be the result of actual phenomenon that we should further investigate. When removing outliers, I try to be as conservative as possible, using the definition of an extreme outlier:
- On the low end, an extreme outlier is below $\text{First Quartile} -1.5 * \text{Interquartile Range}$
- On the high end, an extreme outlier is above $\text{Third Quartile} + 1.5 * \text{Interquartile Range}$
I will define a function that updates all the outliers with the appropriate value in all the columns in the dataset.
In [430]:
#function which takes input a dataframe(x) that can contain both numeric and categorical columns
def fixoutliers(x):
#Get all the column name from the input dataframe x
xColumnNames=x
#keep the labels column as we do't want to alter it
y = xColumnNames['yield']
xColumnNames.drop('yield', axis=1)
print(xColumnNames)
#go throug all collumns ans find whether the values are whiting the setted range:
for j in xColumnNames:
try:
print ("colnames ",j)
xy=x[j]
mydata=pd.DataFrame()
#make an empty list to add the uppdated values
updated=[]
Q1,Q3=np.percentile(xy,[25,75])
IQR=Q3-Q1
minimum=Q1-1.5*IQR #maximum value
maximum=Q3+1.5*IQR #minimum value
for i in xy: #alter columns if they are not in within the range
if(i>maximum):
print("Entering maxim")
i=maximum
updated.append(i)
elif(i<minimum):
print("enterinf minimum")
i=minimum
updated.append(i)
else:
updated.append(i)
x[j]=updated #update the dataframe with the updated values
except:
continue
x['yield']=y #add back the labels column
return x
In [431]:
#fixing outliers
new_data=fixoutliers(data)
week_num yield 1 2 3 4 5 6 \
0 Week 48 FY15 0.57 0.765056 -0.356439 0.197052 0.795395 0 -0.001015
1 Week 49 FY15 0.47 1.062557 -0.156156 -0.234454 0.950919 0 -0.170481
2 Week 50 FY15 0.43 0.961968 -0.276802 0.106828 1.075338 0 -0.004001
3 Week 51 FY15 0.49 0.864231 -0.411954 0.174596 1.168652 0 0.040849
4 Week 52 FY15 0.57 -0.083462 -0.212342 0.110023 1.251599 0 0.021135
5 Week 53 FY15 0.63 -0.456798 -0.264498 0.322492 1.251599 0 0.065378
6 Week 1 FY16 0.57 -0.851854 -0.354455 -0.017179 1.251599 0 -0.038447
7 Week 2 FY16 0.56 -0.596559 -0.225321 -0.090215 1.199757 0 -0.040010
8 Week 3 FY16 0.56 -0.706136 -0.512842 0.145560 1.106443 0 0.007287
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109 0.310102 -0.094483 0.135590 0.225277 -0.350665 0.067770 -0.546253
110 0.203643 0.626478 0.069186 0.149552 -0.061539 0.016429 -0.429644
111 -0.067302 0.427408 -0.567768 -0.530252 0.256933 -0.224993 -0.698875
112 0.362053 -0.227161 0.209911 0.261317 -0.220218 0.145948 -0.739742
113 -0.023610 -0.334035 -0.419251 -0.486912 -0.308793 -0.297192 -0.613146
114 0.376248 -0.126826 0.283245 0.288654 -0.142103 0.209860 -0.382870
115 0.448386 -0.231507 0.546950 0.523869 -0.220795 0.429462 -0.086437
116 0.419390 -0.140384 0.532870 0.463003 -0.154742 0.400858 -0.119698
117 0.642097 -0.201530 0.163459 0.150771 -0.202363 0.096966 -0.073168
118 0.570900 -0.040500 0.301346 0.212235 -0.071163 0.171788 -0.207223
119 0.824939 -0.381920 0.544986 0.499586 -0.353760 0.392382 -0.236824
120 0.715665 -0.550223 0.826875 0.799726 -0.485697 0.547577 0.031591
121 0.594795 -0.495377 0.022718 0.013241 -0.445189 0.028243 -0.112142
122 0.242819 0.062883 0.665258 0.736190 0.007943 0.431251 0.120598
123 -0.753284 -0.546978 0.153732 0.228316 -0.483024 0.107128 0.350547
124 -7.622581 -0.568484 -0.190614 -0.327078 -0.499920 -0.189675 0.228591
125 0.790286 -0.568484 -0.051221 0.064444 -0.499920 -0.045962 -0.299402
126 0.641693 -0.568484 -0.121817 -0.032053 -0.499920 -0.080096 -0.069105
127 0.855329 -0.568484 0.256316 0.373059 -0.499920 0.145416 0.115238
128 0.873747 -0.568484 0.111846 0.232071 -0.499920 0.029533 -0.023697
129 0.404409 -0.568484 0.909496 0.921791 -0.499920 0.521449 0.231754
130 0.104040 0.234788 0.838222 0.763350 0.137666 0.488096 0.148767
28 ... 4311 4312 4313 4314 4315 \
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14 -0.174289 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
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16 -0.205336 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
17 -0.189269 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
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19 -0.197774 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
20 -0.176967 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
21 -0.175426 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
22 -0.255914 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
23 -0.099536 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
24 -0.186920 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
25 -0.201473 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
26 -0.290445 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
27 1.589547 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
28 -0.186074 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
29 -0.244937 ... -1.300000 -1.036887 -0.991674 -1.021653 -0.991608
.. ... ... ... ... ... ... ...
101 -0.094708 ... 0.761415 0.895315 0.979186 0.617179 1.086850
102 -0.187991 ... 0.805642 0.897419 0.967551 0.708609 1.098048
103 -0.183907 ... 0.852889 0.897097 0.951590 0.821816 1.102186
104 -0.183715 ... 0.895266 0.904293 0.945521 0.922058 1.099238
105 -0.196927 ... 0.912609 0.916281 0.948135 1.039547 1.093995
106 -0.178451 ... 0.846672 0.915111 0.942389 1.164177 1.095889
107 -0.184081 ... 0.786231 0.909985 0.937919 1.270715 1.095723
108 -0.194202 ... 0.736868 0.907632 0.936147 1.297961 1.092549
109 -0.210954 ... 0.658923 0.910573 0.937739 1.316671 1.087452
110 -0.220272 ... 0.588668 0.914929 0.942462 1.313575 1.083498
111 5.202379 ... 0.531122 0.922988 0.951931 1.306676 1.080868
112 -0.191934 ... 0.475720 0.930291 0.956570 1.286380 1.077502
113 -0.272724 ... 0.479185 0.938027 0.963563 1.269510 1.071459
114 -0.185526 ... 0.483264 0.947894 0.971050 1.238240 1.058017
115 -0.117440 ... 0.473352 0.954076 0.976147 1.222465 1.048707
116 -0.117279 ... 0.467208 0.958733 0.986059 1.208381 1.037299
117 -0.170590 ... 0.471592 0.966222 0.990921 1.195225 1.030338
118 -0.160196 ... 0.494199 0.966729 0.986089 1.202652 1.020146
119 -0.128534 ... 0.506660 0.975086 0.997385 1.204428 1.011015
120 -0.112119 ... 0.519224 0.984997 1.010336 1.201675 0.997274
121 -0.181742 ... 0.547059 0.990947 1.021911 1.196272 0.989294
122 -0.122126 ... 0.577041 0.995671 1.033017 1.173190 0.980361
123 -0.158770 ... 0.590258 1.000748 1.035648 1.129194 0.973296
124 -0.188754 ... 0.584838 1.009922 1.032677 1.100823 0.955869
125 -0.208053 ... 0.581767 1.036627 1.034719 1.085007 0.948304
126 -0.185659 ... 0.578357 1.063098 1.031508 1.059652 0.944139
127 -0.182614 ... 0.575464 1.097791 1.027777 1.031796 0.942653
128 -0.205313 ... 0.573261 1.132360 1.019764 0.993157 0.945072
129 -0.102906 ... 0.572922 1.168444 1.027290 0.935189 0.942075
130 -0.110286 ... -1.300000 1.200532 -0.991674 0.914338 -0.991608
4316 4317 4318 4319 4320 4321 4322 \
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20 -0.897575 -1.020315 -0.992045 -0.903636 -1.028505 -1.299491 -0.976994
21 -0.897575 -1.020315 -0.992045 -0.903636 -1.028505 -1.299491 -0.976994
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27 -0.897575 -1.020315 -0.992045 -0.903636 -1.028505 -1.299491 -0.976994
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29 -0.897575 -1.020315 -0.992045 -0.903636 -1.028505 -1.299491 -0.976994
.. ... ... ... ... ... ... ...
101 0.987741 0.514887 0.975426 0.852340 0.751311 0.512499 0.152440
102 0.891527 0.588986 0.971639 0.989928 0.777871 0.511422 0.240485
103 0.787822 0.694703 0.971424 1.119715 0.813156 0.501295 0.429349
104 0.727616 0.788585 0.961718 1.236148 0.844085 0.481413 0.642731
105 0.713299 0.894299 0.956574 1.308199 0.905665 0.484429 0.837758
106 0.675068 1.003277 0.950862 1.343988 0.952014 0.518475 0.980703
107 0.644014 1.100489 0.948911 1.374585 1.000674 0.552345 1.130470
108 0.643782 1.135972 0.950950 1.375228 1.051770 0.625149 1.262553
109 0.703062 1.165722 0.952307 1.373026 1.073106 0.687372 1.343983
110 0.733406 1.187909 0.960005 1.372714 1.107556 0.759476 1.417899
111 0.761485 1.244170 0.966768 1.372824 1.163411 0.846829 1.481525
112 0.782324 1.282711 0.970487 1.372767 1.185369 0.896952 1.505954
113 0.827781 1.319238 0.976983 1.372819 1.204925 0.923020 1.527287
114 0.884692 1.323212 0.982194 1.373086 1.199181 0.934144 1.499745
115 0.971599 1.322388 0.992861 1.373033 1.182248 0.913554 1.460750
116 1.079770 1.316875 1.001922 1.357765 1.164776 0.896952 1.408652
117 1.161158 1.297923 1.004830 1.357487 1.165587 0.889877 1.399432
118 1.218265 1.261877 1.005786 1.357701 1.164391 0.890257 1.393241
119 1.343042 1.229553 1.005690 1.333742 1.146382 0.874135 1.337122
120 1.471266 1.199781 1.003107 1.246810 1.124848 0.857498 1.271884
121 1.558683 1.187333 1.009092 1.085649 1.139357 0.881206 1.261494
122 1.662889 1.170188 1.004441 0.861397 1.147749 0.911076 1.233655
123 1.743964 1.141376 1.000174 0.655738 1.136348 0.907971 1.183771
124 1.867913 1.130348 0.995892 0.410991 1.100740 0.883591 1.069320
125 1.900589 1.127729 0.998131 0.103462 1.117973 0.877266 1.057818
126 1.951052 1.118981 1.002292 -0.198036 1.133604 0.882805 1.039624
127 2.057439 1.108187 1.006347 -0.436724 1.146472 0.875983 1.011781
128 2.053308 1.075614 1.005827 -0.601559 1.152569 0.851412 1.011956
129 2.091451 1.021860 1.008149 -0.703088 1.145196 0.833326 0.966913
130 -0.897575 1.003463 -0.992045 -0.903636 1.148980 -1.299491 0.957097
4323 4324 4325 4326 4327 4328 4329 \
0 -1.285899 -0.811748 -0.965811 -0.991597 -0.752612 -1.001958 -0.929988
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29 -1.285899 -0.811748 -0.965811 -0.991597 -0.752612 -1.001958 -0.929988
.. ... ... ... ... ... ... ...
101 0.924107 1.299071 1.231534 1.020582 0.747029 0.722886 0.809215
102 0.965998 1.307196 1.203327 1.011123 0.449254 0.649353 0.766987
103 1.025335 1.350142 1.152890 0.989969 0.786030 0.632033 0.922312
104 1.064819 1.382306 1.139304 0.985695 1.289130 0.727184 1.023473
105 1.077952 1.367314 1.143855 0.985765 1.122053 0.893260 1.118280
106 0.999576 1.405106 1.119387 0.978534 1.103160 1.149989 1.245052
107 0.933066 1.402812 1.118289 0.976016 1.187710 1.373575 1.397867
108 0.874036 1.383816 1.098748 0.971498 1.461453 1.635945 1.565446
109 0.792693 1.390360 1.084691 0.972771 1.903505 1.890322 1.738836
110 0.723736 1.371702 1.088652 0.975252 1.879084 1.949017 1.731190
111 0.665836 1.355264 1.070740 0.976517 1.546954 1.855479 1.764962
112 0.607421 1.393601 1.034318 0.978632 2.115828 1.687225 1.759499
113 0.603043 1.382253 0.978676 0.976987 2.226667 1.368102 1.763305
114 0.583536 1.360821 0.963281 0.981484 2.375056 1.007451 1.730987
115 0.571128 1.358303 0.952569 0.989179 2.047167 0.615043 1.764461
116 0.545632 1.324991 0.951146 0.999509 1.685932 0.399944 1.599606
117 0.550988 1.316453 0.900924 1.001908 2.077410 0.359158 1.461671
118 0.576477 1.297063 0.846523 0.996625 2.651805 0.355279 1.331906
119 0.580475 1.282397 0.838986 1.008356 2.013802 0.357856 1.255270
120 0.585151 1.250100 0.897888 1.031206 1.495501 0.500016 1.162414
121 0.626995 1.236444 0.843934 1.031653 1.204577 0.713956 1.086009
122 0.638088 1.172866 0.874622 1.037555 1.140265 0.928292 0.977448
123 0.623304 1.126065 0.955397 1.042265 1.061346 0.981875 1.029609
124 0.520692 1.061314 1.141393 1.059022 0.587315 1.077188 1.121039
125 0.468945 1.060710 1.263109 1.080595 0.215169 1.104631 1.131481
126 0.396489 1.017658 1.396629 1.095748 0.221711 1.133707 1.134086
127 0.304313 0.972793 1.571572 1.110736 0.194014 1.139673 1.164964
128 0.235881 0.994969 1.763314 1.132965 0.220057 1.251421 1.213085
129 0.158429 1.043038 1.871936 1.153859 0.438814 1.336613 1.231104
130 -1.285899 1.087215 -0.965811 -0.991597 0.697918 1.554784 -0.929988
4330 4331 4332 4333 4334 4335 4336 \
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C:\Users\Daniela\Anaconda3.5\lib\site-packages\numpy\lib\function_base.py:3652: RuntimeWarning: Invalid value encountered in percentile interpolation=interpolation)
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maxim Entering maxim colnames 166 Entering maxim enterinf minimum Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim colnames 167 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 168 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 169 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 170 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 171 Entering maxim Entering maxim Entering maxim Entering maxim colnames 172 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 173 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 174 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 175 Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 176 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 177 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 178 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 179 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 180 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 181 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 182 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 183 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 184 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 185 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 186 Entering maxim Entering maxim colnames 187 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 188 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 189 Entering maxim Entering maxim Entering maxim 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maxim colnames 213 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim colnames 214 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim colnames 215 Entering maxim Entering maxim Entering maxim Entering maxim colnames 216 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 217 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 218 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 219 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 220 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 221 enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 222 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 223 Entering maxim Entering maxim enterinf minimum Entering maxim colnames 224 Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim colnames 225 Entering maxim Entering maxim enterinf minimum Entering maxim enterinf minimum Entering maxim Entering maxim colnames 226 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 227 Entering maxim Entering 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minimum colnames 332 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 333 enterinf minimum enterinf minimum enterinf minimum colnames 334 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 335 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 336 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 337 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 338 Entering maxim enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim colnames 339 Entering maxim colnames 340 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 341 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 342 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 343 Entering maxim colnames 344 enterinf minimum Entering maxim enterinf minimum colnames 345 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 346 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 347 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 348 colnames 349 colnames 350 Entering maxim Entering 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Entering maxim Entering maxim colnames 378 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 379 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 380 colnames 381 enterinf minimum colnames 382 colnames 383 colnames 384 colnames 385 Entering maxim colnames 386 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 387 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 388 Entering maxim Entering maxim colnames 389 colnames 390 colnames 391 enterinf minimum enterinf minimum enterinf minimum colnames 392 colnames 393 colnames 394 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 395 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 396 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 397 enterinf minimum enterinf minimum colnames 398 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 399 Entering maxim Entering maxim Entering maxim Entering maxim colnames 400 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim 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minimum colnames 414 Entering maxim Entering maxim Entering maxim colnames 415 colnames 416 Entering maxim Entering maxim colnames 417 colnames 418 colnames 419 colnames 420 enterinf minimum enterinf minimum enterinf minimum colnames 421 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 422 colnames 423 Entering maxim Entering maxim colnames 424 colnames 425 colnames 426 colnames 427 Entering maxim Entering maxim colnames 428 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum Entering maxim colnames 429 Entering maxim Entering maxim colnames 430 colnames 431 colnames 432 Entering maxim colnames 433 colnames 434 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 435 colnames 436 Entering maxim Entering maxim colnames 437 colnames 438 colnames 439 enterinf minimum enterinf minimum colnames 440 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maxim Entering maxim Entering maxim colnames 1297 colnames 1298 colnames 1299 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1300 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1301 colnames 1302 colnames 1303 colnames 1304 colnames 1305 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1306 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum 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enterinf minimum colnames 1786 colnames 1787 Entering maxim Entering maxim Entering maxim colnames 1788 colnames 1789 colnames 1790 Entering maxim colnames 1791 Entering maxim Entering maxim Entering maxim colnames 1792 enterinf minimum enterinf minimum enterinf minimum colnames 1793 colnames 1794 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1795 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum colnames 1796 colnames 1797 colnames 1798 colnames 1799 enterinf minimum enterinf minimum colnames 1800 colnames 1801 colnames 1802 colnames 1803 colnames 1804 Entering maxim Entering maxim Entering maxim colnames 1805 Entering maxim Entering maxim Entering maxim colnames 1806 Entering maxim Entering maxim colnames 1807 colnames 1808 colnames 1809 colnames 1810 colnames 1811 colnames 1812 colnames 1813 colnames 1814 colnames 1815 colnames 1816 colnames 1817 colnames 1818 colnames 1819 colnames 1820 colnames 1821 colnames 1822 colnames 1823 colnames 1824 colnames 1825 colnames 1826 colnames 1827 colnames 1828 colnames 1829 colnames 1830 colnames 1831 colnames 1832 colnames 1833 colnames 1834 colnames 1835 colnames 1836 colnames 1837 colnames 1838 colnames 1839 colnames 1840 colnames 1841 colnames 1842 colnames 1843 colnames 1844 colnames 1845 colnames 1846 colnames 1847 colnames 1848 colnames 1849 colnames 1850 colnames 1851 colnames 1852 colnames 1853 colnames 1854 colnames 1855 colnames 1856 colnames 1857 colnames 1858 colnames 1859 colnames 1860 colnames 1861 colnames 1862 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 1863 colnames 1864 colnames 1865 colnames 1866 colnames 1867 colnames 1868 Entering maxim Entering maxim colnames 1869 enterinf minimum colnames 1870 colnames 1871 colnames 1872 Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim colnames 1873 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1874 colnames 1875 Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim colnames 1876 enterinf minimum colnames 1877 colnames 1878 colnames 1879 colnames 1880 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1881 colnames 1882 Entering maxim Entering maxim Entering maxim Entering maxim colnames 1883 colnames 1884 colnames 1885 Entering maxim Entering maxim Entering maxim Entering maxim colnames 1886 colnames 1887 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1888 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1889 colnames 1890 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1891 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1892 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim 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maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1926 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1927 colnames 1928 Entering maxim Entering maxim colnames 1929 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1930 colnames 1931 enterinf minimum colnames 1932 colnames 1933 colnames 1934 colnames 1935 colnames 1936 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1937 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1938 colnames 1939 colnames 1940 Entering maxim colnames 1941 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1942 colnames 1943 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1944 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1945 colnames 1946 Entering maxim Entering maxim Entering maxim colnames 1947 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1948 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1949 colnames 1950 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum colnames 1951 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1952 colnames 1953 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1954 colnames 1955 colnames 1956 colnames 1957 colnames 1958 enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum Entering maxim colnames 1959 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum Entering maxim colnames 1960 colnames 1961 colnames 1962 colnames 1963 enterinf minimum enterinf minimum colnames 1964 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1965 colnames 1966 colnames 1967 colnames 1968 colnames 1969 colnames 1970 enterinf minimum colnames 1971 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1972 colnames 1973 Entering maxim Entering maxim colnames 1974 colnames 1975 colnames 1976 colnames 1977 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1978 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 1979 colnames 1980 colnames 1981 colnames 1982 colnames 1983 Entering maxim Entering maxim Entering maxim colnames 1984 enterinf minimum enterinf minimum enterinf minimum colnames 1985 colnames 1986 Entering maxim colnames 1987 colnames 1988 colnames 1989 colnames 1990 colnames 1991 colnames 1992 colnames 1993 colnames 1994 Entering maxim Entering maxim colnames 1995 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1996 Entering maxim Entering maxim Entering maxim colnames 1997 colnames 1998 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 1999 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering 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Entering maxim Entering maxim Entering maxim colnames 2014 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2015 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2016 colnames 2017 colnames 2018 Entering maxim Entering maxim Entering maxim colnames 2019 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2020 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 2021 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2022 colnames 2023 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2024 colnames 2025 colnames 2026 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2027 colnames 2028 enterinf minimum Entering maxim colnames 2029 colnames 2030 colnames 2031 colnames 2032 colnames 2033 Entering maxim Entering maxim Entering maxim colnames 2034 Entering maxim Entering maxim Entering maxim colnames 2035 Entering maxim Entering maxim colnames 2036 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 2037 Entering maxim Entering maxim Entering maxim colnames 2038 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2039 enterinf minimum colnames 2040 colnames 2041 colnames 2042 colnames 2043 Entering maxim Entering maxim Entering maxim colnames 2044 Entering 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minimum enterinf minimum enterinf minimum enterinf minimum colnames 2655 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2656 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2657 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2658 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2659 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2660 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2661 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2662 colnames 2663 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2664 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2665 Entering maxim colnames 2666 colnames 2667 Entering maxim Entering maxim colnames 2668 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2669 colnames 2670 enterinf minimum enterinf minimum enterinf minimum enterinf 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minimum colnames 2729 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2730 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2731 colnames 2732 Entering maxim colnames 2733 colnames 2734 Entering maxim Entering maxim Entering maxim colnames 2735 Entering maxim colnames 2736 enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 2737 colnames 2738 colnames 2739 colnames 2740 colnames 2741 colnames 2742 colnames 2743 colnames 2744 colnames 2745 colnames 2746 colnames 2747 colnames 2748 colnames 2749 colnames 2750 colnames 2751 colnames 2752 colnames 2753 colnames 2754 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim 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colnames 2764 colnames 2765 colnames 2766 colnames 2767 colnames 2768 colnames 2769 colnames 2770 colnames 2771 colnames 2772 colnames 2773 colnames 2774 colnames 2775 colnames 2776 colnames 2777 Entering maxim Entering maxim colnames 2778 colnames 2779 colnames 2780 colnames 2781 colnames 2782 colnames 2783 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2784 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2785 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2786 colnames 2787 colnames 2788 colnames 2789 colnames 2790 colnames 2791 colnames 2792 Entering maxim Entering maxim Entering maxim Entering maxim Entering 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enterinf minimum enterinf minimum enterinf minimum colnames 2966 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2967 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2968 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2969 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2970 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2971 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2972 colnames 2973 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2974 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 2975 colnames 2976 Entering maxim colnames 2977 Entering maxim Entering maxim Entering maxim colnames 2978 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2979 colnames 2980 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2981 colnames 2982 enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2983 colnames 2984 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2985 colnames 2986 Entering maxim enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 2987 enterinf minimum 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3014 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3015 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3016 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3017 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3018 enterinf minimum 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maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3028 colnames 3029 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3030 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3031 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3032 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum 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colnames 3039 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3040 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3041 colnames 3042 Entering maxim colnames 3043 colnames 3044 Entering maxim Entering maxim Entering maxim colnames 3045 colnames 3046 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 3047 colnames 3048 colnames 3049 colnames 3050 colnames 3051 colnames 3052 colnames 3053 colnames 3054 colnames 3055 colnames 3056 colnames 3057 colnames 3058 colnames 3059 colnames 3060 colnames 3061 colnames 3062 colnames 3063 colnames 3064 Entering maxim Entering maxim 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colnames 3171 colnames 3172 colnames 3173 colnames 3174 colnames 3175 colnames 3176 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3177 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3178 colnames 3179 colnames 3180 Entering maxim colnames 3181 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3182 colnames 3183 colnames 3184 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim 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colnames 3263 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3264 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3265 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3266 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3267 Entering maxim enterinf 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colnames 3282 colnames 3283 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3284 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3285 colnames 3286 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3287 Entering maxim Entering maxim Entering maxim colnames 3288 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum 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3315 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3316 Entering maxim Entering maxim colnames 3317 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3318 Entering maxim colnames 3319 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3320 Entering maxim Entering maxim colnames 3321 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3322 enterinf minimum enterinf minimum enterinf 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enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3347 colnames 3348 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3349 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3350 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3351 colnames 3352 Entering maxim colnames 3353 colnames 3354 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum 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enterinf minimum enterinf minimum enterinf minimum colnames 3447 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 3448 colnames 3449 colnames 3450 colnames 3451 colnames 3452 colnames 3453 colnames 3454 colnames 3455 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3456 colnames 3457 colnames 3458 colnames 3459 Entering maxim colnames 3460 Entering maxim Entering maxim colnames 3461 colnames 3462 colnames 3463 colnames 3464 colnames 3465 Entering maxim colnames 3466 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim 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enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3477 colnames 3478 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3479 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3480 colnames 3481 colnames 3482 colnames 3483 colnames 3484 colnames 3485 colnames 3486 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3487 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3488 colnames 3489 colnames 3490 colnames 3491 enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum colnames 3492 Entering maxim Entering maxim colnames 3493 enterinf minimum Entering maxim Entering maxim Entering maxim colnames 3494 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3495 colnames 3496 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3497 enterinf minimum colnames 3498 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3499 Entering maxim Entering maxim colnames 3500 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum colnames 3501 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 3502 colnames 3503 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3504 enterinf minimum colnames 3505 colnames 3506 colnames 3507 colnames 3508 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3509 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 3510 colnames 3511 colnames 3512 colnames 3513 enterinf minimum enterinf minimum colnames 3514 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3515 colnames 3516 Entering maxim colnames 3517 colnames 3518 colnames 3519 colnames 3520 enterinf minimum colnames 3521 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3522 colnames 3523 colnames 3524 colnames 3525 colnames 3526 colnames 3527 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3528 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3529 colnames 3530 colnames 3531 colnames 3532 colnames 3533 colnames 3534 enterinf minimum enterinf minimum enterinf minimum colnames 3535 colnames 3536 Entering maxim Entering maxim colnames 3537 colnames 3538 colnames 3539 colnames 3540 colnames 3541 colnames 3542 colnames 3543 colnames 3544 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3545 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3546 Entering maxim Entering maxim Entering maxim colnames 3547 colnames 3548 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3549 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3550 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3551 colnames 3552 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3553 colnames 3554 colnames 3555 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3556 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3557 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3558 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3559 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3560 colnames 3561 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3562 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3563 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3564 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3565 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3566 colnames 3567 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3568 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3569 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3570 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3571 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3572 colnames 3573 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3574 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3575 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3576 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3577 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3578 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3579 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3580 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3581 colnames 3582 colnames 3583 colnames 3584 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3585 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3586 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3587 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3588 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3589 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3590 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3591 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3592 colnames 3593 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3594 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3595 colnames 3596 enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3597 Entering maxim Entering maxim colnames 3598 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3599 colnames 3600 colnames 3601 colnames 3602 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3603 Entering maxim Entering maxim colnames 3604 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3605 colnames 3606 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3607 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3608 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3609 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3610 colnames 3611 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3612 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3613 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3614 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3615 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3616 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3617 colnames 3618 colnames 3619 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3620 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3621 colnames 3622 colnames 3623 Entering maxim Entering maxim colnames 3624 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3625 colnames 3626 colnames 3627 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3628 Entering maxim Entering maxim colnames 3629 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3630 Entering maxim Entering maxim colnames 3631 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3632 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3633 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3634 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3635 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3636 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3637 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3638 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3639 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3640 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3641 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3642 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3643 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3644 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3645 enterinf minimum enterinf 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minimum enterinf minimum enterinf minimum enterinf minimum colnames 3650 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3651 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3652 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3653 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3654 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3655 enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3656 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3657 colnames 3658 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3659 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3660 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3661 colnames 3662 colnames 3663 colnames 3664 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3665 colnames 3666 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 3667 colnames 3668 colnames 3669 colnames 3670 colnames 3671 colnames 3672 colnames 3673 colnames 3674 colnames 3675 colnames 3676 colnames 3677 Entering maxim Entering maxim colnames 3678 colnames 3679 colnames 3680 colnames 3681 colnames 3682 colnames 3683 colnames 3684 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3685 Entering maxim Entering maxim Entering maxim Entering 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Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3714 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3715 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3716 colnames 3717 colnames 3718 colnames 3719 colnames 3720 colnames 3721 colnames 3722 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3723 colnames 3724 colnames 3725 colnames 3726 colnames 3727 colnames 3728 Entering maxim Entering maxim colnames 3729 colnames 3730 colnames 3731 colnames 3732 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3733 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3734 colnames 3735 Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim colnames 3736 enterinf minimum enterinf minimum enterinf minimum colnames 3737 colnames 3738 colnames 3739 colnames 3740 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3741 colnames 3742 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3743 colnames 3744 enterinf minimum colnames 3745 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3746 colnames 3747 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3748 enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim colnames 3749 colnames 3750 enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3751 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3752 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3753 colnames 3754 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3755 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3756 colnames 3757 Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim colnames 3758 colnames 3759 colnames 3760 colnames 3761 colnames 3762 colnames 3763 colnames 3764 Entering maxim colnames 3765 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3766 colnames 3767 colnames 3768 enterinf minimum colnames 3769 colnames 3770 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3771 colnames 3772 colnames 3773 colnames 3774 colnames 3775 enterinf minimum colnames 3776 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3777 colnames 3778 colnames 3779 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3780 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3781 colnames 3782 enterinf minimum enterinf minimum Entering maxim Entering maxim colnames 3783 colnames 3784 colnames 3785 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3786 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3787 colnames 3788 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3789 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3790 colnames 3791 enterinf minimum colnames 3792 colnames 3793 colnames 3794 colnames 3795 colnames 3796 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3797 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3798 colnames 3799 colnames 3800 Entering maxim colnames 3801 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3802 colnames 3803 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim colnames 3804 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3805 colnames 3806 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3807 enterinf minimum Entering maxim colnames 3808 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3809 Entering maxim colnames 3810 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3811 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim colnames 3812 colnames 3813 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3814 enterinf minimum colnames 3815 colnames 3816 colnames 3817 Entering maxim colnames 3818 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3819 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim colnames 3820 colnames 3821 colnames 3822 colnames 3823 enterinf minimum enterinf minimum colnames 3824 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3825 colnames 3826 Entering maxim colnames 3827 colnames 3828 colnames 3829 colnames 3830 enterinf minimum enterinf minimum colnames 3831 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3832 colnames 3833 colnames 3834 colnames 3835 colnames 3836 colnames 3837 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3838 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3839 colnames 3840 colnames 3841 colnames 3842 colnames 3843 Entering maxim colnames 3844 enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3845 colnames 3846 colnames 3847 colnames 3848 colnames 3849 colnames 3850 colnames 3851 colnames 3852 colnames 3853 colnames 3854 Entering maxim Entering maxim Entering maxim colnames 3855 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3856 colnames 3857 colnames 3858 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3859 enterinf minimum enterinf minimum Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3860 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3861 colnames 3862 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3863 colnames 3864 colnames 3865 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3866 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3867 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3868 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3869 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3870 colnames 3871 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3872 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3873 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3874 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3875 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3876 colnames 3877 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3878 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3879 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3880 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3881 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3882 colnames 3883 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3884 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3885 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3886 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3887 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3888 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3889 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3890 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3891 colnames 3892 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3893 Entering maxim colnames 3894 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3895 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3896 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3897 Entering maxim Entering maxim colnames 3898 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3899 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3900 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3901 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3902 colnames 3903 colnames 3904 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3905 colnames 3906 colnames 3907 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3908 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3909 colnames 3910 colnames 3911 colnames 3912 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3913 Entering maxim colnames 3914 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3915 colnames 3916 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3917 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3918 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3919 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3920 Entering maxim colnames 3921 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3922 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3923 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3924 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3925 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3926 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3927 Entering maxim Entering maxim colnames 3928 colnames 3929 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3930 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3931 Entering maxim colnames 3932 colnames 3933 colnames 3934 colnames 3935 colnames 3936 colnames 3937 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3938 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3939 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3940 Entering maxim Entering maxim Entering maxim Entering maxim colnames 3941 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3942 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3943 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3944 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3945 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3946 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3947 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3948 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3949 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3950 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3951 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3952 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3953 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3954 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3955 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3956 colnames 3957 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3958 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3959 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3960 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3961 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3962 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3963 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3964 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3965 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3966 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3967 colnames 3968 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3969 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3970 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3971 colnames 3972 colnames 3973 colnames 3974 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 3975 colnames 3976 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 3977 colnames 3978 colnames 3979 colnames 3980 colnames 3981 colnames 3982 colnames 3983 colnames 3984 colnames 3985 colnames 3986 colnames 3987 colnames 3988 colnames 3989 colnames 3990 colnames 3991 colnames 3992 colnames 3993 colnames 3994 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3995 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3996 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 3997 colnames 3998 colnames 3999 colnames 4000 colnames 4001 colnames 4002 colnames 4003 colnames 4004 colnames 4005 colnames 4006 colnames 4007 colnames 4008 colnames 4009 colnames 4010 colnames 4011 colnames 4012 colnames 4013 colnames 4014 colnames 4015 colnames 4016 colnames 4017 colnames 4018 colnames 4019 colnames 4020 colnames 4021 colnames 4022 colnames 4023 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4024 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4025 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4026 colnames 4027 colnames 4028 colnames 4029 colnames 4030 colnames 4031 colnames 4032 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4033 colnames 4034 colnames 4035 colnames 4036 colnames 4037 colnames 4038 Entering maxim Entering maxim colnames 4039 enterinf minimum colnames 4040 colnames 4041 colnames 4042 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4043 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4044 colnames 4045 Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim colnames 4046 enterinf minimum colnames 4047 colnames 4048 colnames 4049 colnames 4050 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4051 colnames 4052 Entering maxim Entering maxim Entering maxim Entering maxim colnames 4053 colnames 4054 colnames 4055 Entering maxim Entering maxim Entering maxim Entering maxim colnames 4056 colnames 4057 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4058 enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4059 colnames 4060 enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4061 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4062 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4063 colnames 4064 enterinf minimum Entering maxim Entering maxim colnames 4065 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4066 colnames 4067 Entering maxim Entering maxim Entering maxim colnames 4068 colnames 4069 colnames 4070 Entering maxim colnames 4071 colnames 4072 colnames 4073 colnames 4074 colnames 4075 Entering maxim Entering maxim Entering maxim colnames 4076 colnames 4077 colnames 4078 enterinf minimum enterinf minimum Entering maxim colnames 4079 colnames 4080 Entering maxim Entering maxim colnames 4081 colnames 4082 colnames 4083 colnames 4084 colnames 4085 enterinf minimum enterinf minimum enterinf minimum colnames 4086 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4087 colnames 4088 colnames 4089 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4090 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4091 colnames 4092 colnames 4093 colnames 4094 colnames 4095 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4096 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4097 colnames 4098 Entering maxim Entering maxim colnames 4099 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4100 colnames 4101 enterinf minimum colnames 4102 colnames 4103 colnames 4104 colnames 4105 colnames 4106 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4107 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4108 colnames 4109 colnames 4110 Entering maxim colnames 4111 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4112 colnames 4113 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4114 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4115 colnames 4116 Entering maxim Entering maxim Entering maxim colnames 4117 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4118 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4119 colnames 4120 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum colnames 4121 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4122 colnames 4123 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4124 colnames 4125 colnames 4126 colnames 4127 colnames 4128 enterinf minimum enterinf minimum enterinf minimum Entering maxim enterinf minimum enterinf minimum Entering maxim colnames 4129 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum Entering maxim colnames 4130 colnames 4131 colnames 4132 colnames 4133 enterinf minimum enterinf minimum colnames 4134 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4135 colnames 4136 colnames 4137 colnames 4138 colnames 4139 colnames 4140 enterinf minimum colnames 4141 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4142 colnames 4143 Entering maxim Entering maxim colnames 4144 colnames 4145 colnames 4146 colnames 4147 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4148 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4149 colnames 4150 colnames 4151 colnames 4152 colnames 4153 Entering maxim Entering maxim Entering maxim colnames 4154 enterinf minimum enterinf minimum enterinf minimum colnames 4155 colnames 4156 Entering maxim colnames 4157 colnames 4158 colnames 4159 colnames 4160 colnames 4161 colnames 4162 colnames 4163 colnames 4164 Entering maxim colnames 4165 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4166 colnames 4167 colnames 4168 Entering maxim Entering maxim Entering maxim colnames 4169 enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4170 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4171 colnames 4172 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4173 colnames 4174 colnames 4175 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4176 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4177 colnames 4178 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4179 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4180 colnames 4181 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4182 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4183 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4184 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4185 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4186 colnames 4187 colnames 4188 enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4189 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4190 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4191 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4192 colnames 4193 Entering maxim Entering maxim Entering maxim Entering maxim colnames 4194 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4195 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4196 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4197 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4198 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4199 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4200 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4201 colnames 4202 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4203 Entering maxim colnames 4204 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4205 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4206 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4207 Entering maxim colnames 4208 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4209 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4210 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4211 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4212 colnames 4213 colnames 4214 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4215 colnames 4216 colnames 4217 enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4218 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4219 colnames 4220 colnames 4221 colnames 4222 enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4223 Entering maxim Entering maxim colnames 4224 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4225 colnames 4226 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4227 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4228 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4229 Entering maxim colnames 4230 colnames 4231 Entering maxim Entering maxim Entering maxim Entering maxim colnames 4232 Entering maxim Entering maxim Entering maxim Entering maxim colnames 4233 enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4234 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4235 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4236 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4237 Entering maxim Entering maxim Entering maxim Entering maxim colnames 4238 colnames 4239 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4240 colnames 4241 Entering maxim colnames 4242 colnames 4243 colnames 4244 colnames 4245 colnames 4246 colnames 4247 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4248 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4249 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4250 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4251 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4252 colnames 4253 enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4254 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4255 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4256 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4257 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4258 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4259 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4260 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4261 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4262 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4263 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4264 colnames 4265 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4266 colnames 4267 Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4268 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4269 colnames 4270 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4271 Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4272 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4273 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4274 Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4275 enterinf minimum Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4276 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4277 colnames 4278 colnames 4279 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4280 Entering maxim Entering maxim enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum colnames 4281 colnames 4282 colnames 4283 colnames 4284 Entering maxim colnames 4285 Entering maxim Entering maxim Entering maxim colnames 4286 enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum enterinf minimum Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim enterinf minimum colnames 4287 colnames 4288 colnames 4289 colnames 4290 colnames 4291 colnames 4292 colnames 4293 colnames 4294 colnames 4295 colnames 4296 colnames 4297 colnames 4298 colnames 4299 colnames 4300 colnames 4301 colnames 4302 colnames 4303 colnames 4304 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4305 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4306 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4307 colnames 4308 colnames 4309 colnames 4310 colnames 4311 colnames 4312 colnames 4313 colnames 4314 colnames 4315 colnames 4316 colnames 4317 colnames 4318 colnames 4319 colnames 4320 colnames 4321 colnames 4322 colnames 4323 colnames 4324 colnames 4325 colnames 4326 colnames 4327 colnames 4328 colnames 4329 colnames 4330 colnames 4331 colnames 4332 colnames 4333 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4334 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4335 Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim Entering maxim colnames 4336 colnames 4337 colnames 4338 colnames 4339 colnames 4340
In [432]:
#updated dataframe after fixing outliers
new_data.head()
Out[432]:
| week_num | yield | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | ... | 4311 | 4312 | 4313 | 4314 | 4315 | 4316 | 4317 | 4318 | 4319 | 4320 | 4321 | 4322 | 4323 | 4324 | 4325 | 4326 | 4327 | 4328 | 4329 | 4330 | 4331 | 4332 | 4333 | 4334 | 4335 | 4336 | 4337 | 4338 | 4339 | 4340 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Week 48 FY15 | 0.57 | 0.765056 | -0.356439 | 0.197052 | 0.795395 | 0 | -0.001015 | 0.196354 | 0.081835 | 0.950103 | -0.063364 | -0.829207 | -0.241069 | -0.331018 | -0.330876 | 0.018767 | 0.260456 | -0.067674 | 0.525733 | -0.131478 | -0.474496 | -0.229206 | -0.436584 | -0.391205 | -0.291944 | -0.394279 | 0.015729 | -0.661840 | -0.221699 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 1 | Week 49 FY15 | 0.47 | 1.062557 | -0.156156 | -0.234454 | 0.950919 | 0 | -0.170481 | -0.057973 | 0.362018 | 0.590900 | -0.030287 | -0.808753 | 0.520046 | -0.331018 | 1.098410 | -0.036730 | 1.044749 | -0.154249 | 0.656448 | -0.159455 | -0.758297 | -0.190549 | -0.332570 | 0.349147 | 0.341943 | -0.310972 | 0.303210 | -0.558677 | -0.133704 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 2 | Week 50 FY15 | 0.43 | 0.961968 | -0.276802 | 0.106828 | 1.075338 | 0 | -0.004001 | 0.110006 | 0.201414 | 0.516113 | -0.016122 | -0.772992 | 0.347968 | -0.331018 | 0.772261 | 0.225179 | 0.792992 | -0.104244 | 0.553572 | -0.175071 | -0.563206 | 0.008438 | -0.469626 | 0.413091 | 0.442866 | -0.420743 | 0.414846 | -0.595874 | -0.101545 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 3 | Week 51 FY15 | 0.49 | 0.864231 | -0.411954 | 0.174596 | 1.168652 | 0 | 0.040849 | 0.032461 | 0.311033 | 0.605321 | -0.023123 | -0.711317 | -0.098511 | -0.331018 | -0.485911 | -0.064177 | 0.610803 | -0.110098 | 0.553419 | -0.201746 | 0.084896 | -0.078933 | -0.542146 | 0.656361 | 0.552064 | -0.478825 | 0.474788 | -0.449464 | -0.085681 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 4 | Week 52 FY15 | 0.57 | -0.083462 | -0.212342 | 0.110023 | 1.251599 | 0 | 0.021135 | -0.133111 | 0.152851 | 0.944587 | -0.014222 | -0.840133 | 0.974383 | -0.331018 | 0.471113 | -0.287214 | 0.642511 | -0.140182 | 0.083886 | -0.212156 | -0.806272 | -0.432690 | -0.568484 | 0.453516 | 0.341360 | -0.499920 | 0.375777 | -0.458860 | -0.107713 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
5 rows × 4342 columns
In [433]:
# Statistics for each column in updated dataframe
new_data.describe()
Out[433]:
| yield | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | ... | 4311 | 4312 | 4313 | 4314 | 4315 | 4316 | 4317 | 4318 | 4319 | 4320 | 4321 | 4322 | 4323 | 4324 | 4325 | 4326 | 4327 | 4328 | 4329 | 4330 | 4331 | 4332 | 4333 | 4334 | 4335 | 4336 | 4337 | 4338 | 4339 | 4340 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| count | 115.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.0 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 1.310000e+02 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | ... | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 | 131.000000 |
| mean | 0.675391 | 0.012175 | -0.319763 | 0.032254 | 0.026639 | 0.0 | -0.113118 | 0.052832 | -0.019941 | 0.052197 | -0.102723 | -0.007656 | -0.122928 | -3.310184e-01 | -0.008835 | 0.006114 | 0.008816 | -0.071727 | 0.005120 | -0.197256 | -0.002396 | 0.132116 | -0.140989 | 0.072317 | 0.094681 | -0.175510 | 0.108733 | -0.181117 | -0.167583 | -0.003357 | ... | 0.019847 | -0.018212 | 0.015140 | -0.012253 | 0.015139 | 0.013703 | -0.013526 | 0.015146 | 0.013796 | -0.017083 | 0.019840 | -0.013002 | 0.019632 | -0.017392 | 0.014745 | 0.015139 | -0.010341 | -0.023997 | 0.014198 | 0.014973 | 0.011159 | 0.015135 | -0.041483 | -0.050189 | -0.181834 | 0.015146 | -0.016099 | 0.014991 | -0.016266 | -0.018191 |
| std | 0.173095 | 0.992832 | 0.172818 | 0.974747 | 0.987683 | 0.0 | 0.194482 | 0.523170 | 0.296463 | 0.550490 | 0.034916 | 0.952971 | 0.473595 | 3.343455e-16 | 1.004106 | 0.272519 | 1.007099 | 0.249999 | 0.973037 | 0.030170 | 0.938170 | 0.408033 | 0.489089 | 0.440006 | 0.394875 | 0.362779 | 0.298533 | 0.471939 | 0.055647 | 0.943179 | ... | 0.998339 | 1.000419 | 1.003851 | 1.006448 | 1.003852 | 1.005233 | 1.005352 | 1.003845 | 1.005148 | 1.001739 | 0.998349 | 1.005716 | 0.998624 | 1.001403 | 1.004245 | 1.003852 | 1.007746 | 0.992102 | 1.004773 | 1.004018 | 1.007339 | 1.003856 | 0.912571 | 0.839993 | 0.465584 | 1.003845 | 1.002811 | 1.004001 | 1.002566 | 1.000447 |
| min | 0.380000 | -2.276594 | -0.600320 | -1.344745 | -1.765569 | 0.0 | -0.428650 | -1.146657 | -0.723159 | -1.156419 | -0.186073 | -0.885389 | -1.071456 | -3.310184e-01 | -1.373330 | -0.642826 | -2.231267 | -0.415026 | -2.738574 | -0.240134 | -1.307903 | -0.865598 | -0.568484 | -0.990475 | -0.914732 | -0.499920 | -0.684218 | -0.739742 | -0.305234 | -1.150176 | ... | -1.300000 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.991360 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 25% | 0.525000 | -0.726656 | -0.445459 | -0.786582 | -0.733926 | 0.0 | -0.277096 | -0.212699 | -0.212299 | -0.212930 | -0.125539 | -0.753347 | -0.460810 | -3.310184e-01 | -0.739639 | -0.160585 | -0.418765 | -0.286940 | -0.653723 | -0.220940 | -0.637095 | -0.097085 | -0.544300 | -0.175117 | -0.156850 | -0.474049 | -0.070744 | -0.549544 | -0.202120 | -0.805935 | ... | -1.300000 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.991360 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 50% | 0.650000 | 0.131757 | -0.351201 | -0.017179 | 0.162930 | 0.0 | -0.149212 | 0.104851 | -0.024938 | 0.185155 | -0.110266 | -0.408105 | -0.229996 | -3.310184e-01 | -0.285495 | -0.025708 | 0.314754 | -0.104244 | 0.258382 | -0.201746 | -0.243295 | 0.129581 | -0.334035 | 0.083081 | 0.126280 | -0.310972 | 0.096966 | -0.317995 | -0.174289 | -0.164899 | ... | 0.588668 | 0.894109 | 0.936147 | 0.457846 | 0.862280 | -0.260324 | 0.470975 | 0.948911 | -0.703088 | 0.537219 | 0.617484 | -0.121098 | 0.582681 | -0.811748 | 0.492216 | 0.934064 | -0.752612 | 0.357856 | -0.353018 | 0.534925 | -0.730907 | 0.927847 | -0.178247 | -0.202833 | -0.333432 | 0.927506 | 0.839520 | 0.742849 | 0.401413 | -0.800299 |
| 75% | 0.820000 | 0.868233 | -0.249513 | 0.689194 | 0.930182 | 0.0 | 0.022078 | 0.409939 | 0.128273 | 0.416063 | -0.081012 | 0.559834 | 0.113267 | -3.310184e-01 | 0.653403 | 0.160909 | 0.789570 | 0.104917 | 0.736178 | -0.179883 | 0.497446 | 0.415257 | 0.155760 | 0.368455 | 0.348405 | 0.045178 | 0.338238 | 0.054899 | -0.133377 | 0.484090 | ... | 0.842512 | 0.941332 | 0.990198 | 1.010513 | 1.013364 | 0.861445 | 1.009165 | 1.001910 | 1.148301 | 0.961256 | 0.861348 | 1.022361 | 0.879483 | 1.184753 | 0.932457 | 0.986209 | 0.903354 | 0.870551 | 0.958373 | 1.049698 | 1.022801 | 0.985124 | 0.253157 | 0.328903 | 0.009021 | 1.000359 | 0.960832 | 0.950500 | 0.838910 | 1.095020 |
| max | 1.070000 | 1.711989 | 0.044404 | 2.743958 | 1.251599 | 0.0 | 0.470839 | 1.142294 | 0.639133 | 1.359553 | -0.014222 | 2.529605 | 0.974383 | -3.310184e-01 | 2.742967 | 0.643150 | 1.312071 | 0.692702 | 2.087265 | -0.118297 | 2.199259 | 0.873747 | 1.205849 | 1.102200 | 1.056587 | 0.824019 | 0.828886 | 0.961564 | -0.030263 | 2.419128 | ... | 0.995714 | 1.200532 | 1.182414 | 1.316671 | 1.102186 | 2.091451 | 1.323212 | 1.125495 | 1.559355 | 1.204925 | 0.968651 | 1.527287 | 1.077952 | 1.405106 | 1.871936 | 1.188678 | 2.651805 | 1.949017 | 1.764962 | 1.386134 | 1.936779 | 1.223061 | 1.794064 | 1.909268 | 0.836052 | 1.187765 | 1.114567 | 1.424802 | 1.683484 | 1.713457 |
8 rows × 4341 columns
In [434]:
# Histogram Plot of variable 1
figsize(8, 8)
plt.hist(data['1'].dropna(), bins = 20, edgecolor = 'black');
plt.xlabel('1');
plt.ylabel('Count'); plt.title('Variable 1 Distribution');
This plot looks close to normally distributed with a long tail on the left side (it has a negative skew).
In [435]:
figsize(8, 8)
# Histogram of the yield
plt.style.use('fivethirtyeight')
plt.hist(new_data['yield'].dropna(), bins = 100, edgecolor = 'k');
plt.xlabel('yield'); plt.ylabel('Number of Yelds');
plt.title('Yield Distribution');
The yield label seems also to have a normal distribution.
Looking for Relationships¶
Since there are no categorical values to plot against the yield variable's values on a kernel density estimation plot, I will to focus on the numerical columns for predicting the yield.
Correlations between Features and Target¶
In order to quantify correlations between the features (variables) and the target (yield variable), we can calculate the Pearson correlation coefficient. This is a measure of the strength and direction of a linear relationship between two variables: a value of -1 means the two variables are perfectly negatively linearly correlated and a value of +1 means the two variables are perfectly positively linearly correlated.
In [436]:
# Find all correlations and sort
correlations_data = new_data.corr()['yield'].sort_values()
# Print the most negative correlations
print(correlations_data.head(15), '\n')
# Print the most positive correlations
print(correlations_data.tail(15))
4 -0.803702 4126 -0.792725 1956 -0.792725 314 -0.789987 2484 -0.789987 3816 -0.788481 1646 -0.788481 3506 -0.783567 1336 -0.783567 4100 -0.776829 1930 -0.776829 2794 -0.771485 624 -0.771485 3196 -0.766431 1026 -0.766431 Name: yield, dtype: float64 5 NaN 315 NaN 625 NaN 935 NaN 1245 NaN 1555 NaN 1865 NaN 2175 NaN 2485 NaN 2512 NaN 2795 NaN 3105 NaN 3415 NaN 3725 NaN 4035 NaN Name: yield, dtype: float64
Correlation is calculated as folows : $cor(i,j) = cov(i,j)/[stdev(i)*stdev(j)]$
If the values of the ith or jth variable do not vary, then the respective standard deviation will be zero and so will the denominator of the fraction. Thus, the correlation will be NaN. If there is no correlation, then in my opinion, the variables in cause should not be used in predicting the yield values.
In [437]:
#drop the columns with constant value of zero
new_data.drop(['5','315','625','935','1245','1555','1865','2175','2485','2795','3105','3415','3725','4035'], axis=1, inplace=True)
In [438]:
new_data.head()
Out[438]:
| week_num | yield | 1 | 2 | 3 | 4 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | ... | 4311 | 4312 | 4313 | 4314 | 4315 | 4316 | 4317 | 4318 | 4319 | 4320 | 4321 | 4322 | 4323 | 4324 | 4325 | 4326 | 4327 | 4328 | 4329 | 4330 | 4331 | 4332 | 4333 | 4334 | 4335 | 4336 | 4337 | 4338 | 4339 | 4340 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | Week 48 FY15 | 0.57 | 0.765056 | -0.356439 | 0.197052 | 0.795395 | -0.001015 | 0.196354 | 0.081835 | 0.950103 | -0.063364 | -0.829207 | -0.241069 | -0.331018 | -0.330876 | 0.018767 | 0.260456 | -0.067674 | 0.525733 | -0.131478 | -0.474496 | -0.229206 | -0.436584 | -0.391205 | -0.291944 | -0.394279 | 0.015729 | -0.661840 | -0.221699 | -1.141306 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 1 | Week 49 FY15 | 0.47 | 1.062557 | -0.156156 | -0.234454 | 0.950919 | -0.170481 | -0.057973 | 0.362018 | 0.590900 | -0.030287 | -0.808753 | 0.520046 | -0.331018 | 1.098410 | -0.036730 | 1.044749 | -0.154249 | 0.656448 | -0.159455 | -0.758297 | -0.190549 | -0.332570 | 0.349147 | 0.341943 | -0.310972 | 0.303210 | -0.558677 | -0.133704 | -1.096242 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 2 | Week 50 FY15 | 0.43 | 0.961968 | -0.276802 | 0.106828 | 1.075338 | -0.004001 | 0.110006 | 0.201414 | 0.516113 | -0.016122 | -0.772992 | 0.347968 | -0.331018 | 0.772261 | 0.225179 | 0.792992 | -0.104244 | 0.553572 | -0.175071 | -0.563206 | 0.008438 | -0.469626 | 0.413091 | 0.442866 | -0.420743 | 0.414846 | -0.595874 | -0.101545 | -1.017314 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 3 | Week 51 FY15 | 0.49 | 0.864231 | -0.411954 | 0.174596 | 1.168652 | 0.040849 | 0.032461 | 0.311033 | 0.605321 | -0.023123 | -0.711317 | -0.098511 | -0.331018 | -0.485911 | -0.064177 | 0.610803 | -0.110098 | 0.553419 | -0.201746 | 0.084896 | -0.078933 | -0.542146 | 0.656361 | 0.552064 | -0.478825 | 0.474788 | -0.449464 | -0.085681 | -0.889290 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
| 4 | Week 52 FY15 | 0.57 | -0.083462 | -0.212342 | 0.110023 | 1.251599 | 0.021135 | -0.133111 | 0.152851 | 0.944587 | -0.014222 | -0.840133 | 0.974383 | -0.331018 | 0.471113 | -0.287214 | 0.642511 | -0.140182 | 0.083886 | -0.212156 | -0.806272 | -0.432690 | -0.568484 | 0.453516 | 0.341360 | -0.499920 | 0.375777 | -0.458860 | -0.107713 | -1.150176 | ... | -1.3 | -1.036887 | -0.991674 | -1.021653 | -0.991608 | -0.897575 | -1.020315 | -0.992045 | -0.903636 | -1.028505 | -1.299491 | -0.976994 | -1.285899 | -0.811748 | -0.965811 | -0.991597 | -0.752612 | -1.001958 | -0.929988 | -0.980759 | -0.730907 | -0.99136 | -0.774115 | -0.724674 | -0.542333 | -0.992039 | -1.036513 | -0.981902 | -0.995691 | -0.800299 |
5 rows × 4328 columns
In [439]:
#correlation coeficient for data without the variables with constant value
# Find all correlations
correlations_data = new_data.corr()['yield'].sort_values()
# Print the most negative correlations
print(correlations_data.head(15), '\n')
# Print the most positive correlations
print(correlations_data.tail(30))
4 -0.803702 4126 -0.792725 1956 -0.792725 314 -0.789987 2484 -0.789987 3816 -0.788481 1646 -0.788481 3506 -0.783567 1336 -0.783567 4100 -0.776829 1930 -0.776829 2794 -0.771485 624 -0.771485 3196 -0.766431 1026 -0.766431 Name: yield, dtype: float64 2801 0.718458 2819 0.718631 631 0.718646 4047 0.724399 1877 0.724399 1863 0.731834 4033 0.731834 3723 0.735511 1553 0.735511 1567 0.735911 3737 0.735911 1243 0.740894 3413 0.740894 2483 0.745065 313 0.745065 1257 0.747874 3427 0.747874 3103 0.754794 933 0.754794 623 0.756456 2793 0.756456 17 0.757064 947 0.759665 3117 0.759665 2807 0.768588 637 0.768588 2497 0.773458 327 0.773458 yield 1.000000 2512 NaN Name: yield, dtype: float64
To account for possible non-linear relationships, we can take square root and natural log transformations of the features and then calculate the correlation coefficients with the yield. Bellow there is the function to performs the variables' square root and log transformation; in the case of this data set where there are many variables, the process is resourcess consuming and I won't perfom it.
In [440]:
# Select the numeric columns
#numeric_subset = new_data.select_dtypes('number')
# Create columns with square root and log of numeric columns
#for col in numeric_subset.columns:
#Skip the yield column
#if col == ['yield','week_num']:
#next
#else:
#numeric_subset['sqrt_' + str(col)] = np.sqrt(numeric_subset[col])
#numeric_subset['log_' + str(col)] = np.log(numeric_subset[col])
# Drop buildings without an energy star score
#features = numeric_subset.dropna(subset = ['yield'])
# Find correlations with the score
#correlations = features.corr()['yeld'].dropna().sort_values()
In [441]:
#save the data set with a new name
features=new_data.copy()
Pairs Plot¶
As a final step for exploratory data analysis, we can make a pairs plot between several different variables. The Pairs Plot is a great way to examine many variables at once as it shows scatterplots between pairs of variables and histograms of single variables on the diagonal.
Using the seaborn PairGrid function, we can map different plots on to the three aspects of the grid. The upper triangle will have scatterplots, the diagonal will show histograms, and the lower triangle will show both the correlation coefficient between two variables and a 2-D kernel density estimate of the two variables.
In [442]:
# Extract the columns to plot
plot_data = features[['yield', '4',
'1956', '4126']]
# Replace the inf with nan
plot_data = plot_data.replace({np.inf: np.nan, -np.inf: np.nan})
# Drop na values
plot_data = plot_data.dropna()
# Function to calculate correlation coefficient between two columns
def corr_func(x, y, **kwargs):
r = np.corrcoef(x, y)[0][1]
ax = plt.gca()
ax.annotate("r = {:.2f}".format(r),
xy=(.2, .8), xycoords=ax.transAxes,
size = 20)
# Create the pairgrid object
grid = sns.PairGrid(data = plot_data, size = 3)
# Upper is a scatter plot
grid.map_upper(plt.scatter, color = 'red', alpha = 0.6)
# Diagonal is a histogram
grid.map_diag(plt.hist, color = 'red', edgecolor = 'black')
# Bottom is correlation and density plot
grid.map_lower(corr_func);
grid.map_lower(sns.kdeplot, cmap = plt.cm.Reds)
# Title for entire plot
plt.suptitle('Pairs Plot of Hypothetical Weather Data', size = 36, y = 1.02);
C:\Users\Daniela\Anaconda3.5\lib\site-packages\seaborn\axisgrid.py:1241: UserWarning: The `size` paramter has been renamed to `height`; please update your code. warnings.warn(UserWarning(msg)) C:\Users\Daniela\Anaconda3.5\lib\site-packages\scipy\stats\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result. return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval
To interpret the relationships in the plot, we can look for where the variables in one row intersect with the variables in one column. For example, to find the relationship between yield and 4126, we look at the yield column and find 4126 row. At the intersection (the lower left plot) we see that the score has a -0.79 correlation coefficient with this varible. If we look at the upper right plot, we can see a scatterplot of this relationship.
Feature Engineering and Selection¶
For feature selection, I will remove the collinear features. I will discuss collinearity (also called multicollinearity) when I get to that process!
First will plot the collinear feature into a heat map for inspection.
In [443]:
sns.heatmap(features.corr(), cmap="coolwarm")
Out[443]:
<matplotlib.axes._subplots.AxesSubplot at 0x288ba281a58>
It seems that the correlation coefficient has maximum value around 0.8 (both positive and negative).
Removing Collinear Features¶
Highly collinear features have a significant correlation coefficent between them. Having highly correlated fetures (positive and negative) can impact the performance of model by multicollinearity.
This can lead to misleading results, but luckily decision trees and boosted trees algorithms are immune to multicollinearity by nature.
Here I will remove the features that have a colinearity coefficient of 0.75 (which is close to the maximum coeficient, but many of the features have coefficient around 0.8). Setting up a higher or lower threshold won't help impove much in algorithm performance. As mentioned above, for this specific problem removing colinear feature is not necessary, as in the end I will be using a boosted tree type algortihm; it mostly helps in decreasing resources consume, as we will end up with less features to feed the algorithm.
In [444]:
def remove_collinear_features(x, threshold):
'''
Objective:
Remove collinear features in a dataframe with a correlation coefficient
greater than the threshold. Removing collinear features can help a model
to generalize and improves the interpretability of the model.
Inputs:
threshold: any features with correlations greater than this value are removed
Output:
dataframe that contains only the non-highly-collinear features
'''
# Dont want to remove correlations between Energy Star Score
y = x['yield']
x = x.drop(columns = ['yield'])
# Calculate the correlation matrix
corr_matrix = x.corr()
iters = range(len(corr_matrix.columns) - 1)
drop_cols = []
# Iterate through the correlation matrix and compare correlations
for i in iters:
for j in range(i):
item = corr_matrix.iloc[j:(j+1), (i+1):(i+2)]
col = item.columns
row = item.index
val = abs(item.values)
# If correlation exceeds the threshold
if val >= threshold:
# Print the correlated features and the correlation value
# print(col.values[0], "|", row.values[0], "|", round(val[0][0], 2))
drop_cols.append(col.values[0])
# Drop one of each pair of correlated columns
drops = set(drop_cols)
x = x.drop(columns = drops)
# Add the score back in to the data
x['yield'] = y
return x
In [445]:
# Remove the collinear features above a specified correlation coefficient
features = remove_collinear_features(features, 0.75);
C:\Users\Daniela\Anaconda3.5\lib\site-packages\ipykernel_launcher.py:33: RuntimeWarning: invalid value encountered in greater_equal
Additional Feature Selection¶
There are plenty of more methods for feature selection. Some popular methods include principal components analysis (PCA) which transforms the features into a reduced number of dimensions that preserve the greatest variance, or independent components analysis (ICA) which aims to find the independent sources in a set of features. However, while these methods are effective at reducing the number of features, they create new features that have no physical meaning and hence make interpreting a model nearly impossible.
In [446]:
features.to_csv('features.csv', index = False)
features = pd.read_csv('features.csv')
features.shape
Out[446]:
(131, 554)
Split Into Training and Testing Sets¶
In machine learning, we always need to separate our features into two sets:
- Training set which we provide to our model during training along with the answers so it can learn a mapping between the features and the target; I will split again this set into a train and validation set, as the test set is not containing the target values column. Since we are not dealling with classification and class imbalance, we do not need to do stratified subsampling.
- Testing set which we use to evaluate the mapping learned by the model. The model has never seen the answers on the testing set, but instead, must make predictions using only the features.
Splitting the data into a random training and validation set is simple using scikit-learn. We can set the random state of the split to ensure consistent results.
In [447]:
#split the data set into training and testing set as was indicated in the problem statement
train = features.iloc[0:115].copy()
test = features.iloc[115:131].copy()
#test = test.drop(columns='yield')
# Display sizes of data
print('Training Feature Size: ', train.shape)
print('Testing Feature Size: ', test.shape)
Training Feature Size: (115, 554) Testing Feature Size: (16, 554)
In [448]:
#save the training and testing set into .csv files
train.to_csv('train_final', index=False)
test.to_csv('test_final', index=False)
In [449]:
#save the target column and convert y to one-dimensional array (vector)
y =np.array(train['yield'])
# Remove the ids and target and convert X to array (vector)
X =np.array (train.drop(columns = ['week_num', 'yield']))
In [450]:
def mape(y_true, y_pred):
return (np.mean(abs((y_true - y_pred)/y_true)))*100
Models to Evaluate¶
We will compare five different machine learning models using the great Scikit-Learn library:
- Base-line model which is a naive gues based on median values
- Linear Regression
- Random Forest Regression
- Light Gradient Boosting Regression
- Gradient Boosting Regression
- K-Nearest Neighbors Regression
- Support Vector Machine Regression
In [451]:
from sklearn.model_selection import train_test_split
x_train, x_valid, y_train, y_valid = train_test_split(X, y, test_size=0.2, random_state=42)
baseline_guess = np.median(y)
err = mape(y_valid, baseline_guess)
print('MAPE = ' + str(err))
MAPE_baseline = err
MAPE = 21.51906573076165
In [452]:
# Takes in a model, trains the model, and evaluates the model on the validation set
def fit_and_evaluate(model):
x_train, x_valid, y_train, y_valid = train_test_split(X, y, test_size=0.2, random_state=42)
# Train the model
model.fit(x_train, y_train)
# Make predictions and evalute
preds = model.predict(x_valid)
err = mape(y_valid, preds)
print('MAPE = ' + str(err))
MAPE=err
# Return the performance metric list
return MAPE
In [453]:
lr = LinearRegression()
lr_mape = fit_and_evaluate(lr)
MAPE = 16.15309448780313
In [454]:
random_forest = RandomForestRegressor(random_state=60)
random_forest_mape = fit_and_evaluate(random_forest)
MAPE = 8.99545317633642
In [455]:
knn = KNeighborsRegressor(n_neighbors=5)
knn_mape = fit_and_evaluate(knn)
MAPE = 15.66753359085877
In [456]:
gradient_boosted = GradientBoostingRegressor()
gradient_boosted_mape = fit_and_evaluate(gradient_boosted)
MAPE = 8.603293440600064
In [457]:
lgbm = lgb.LGBMRegressor()
lgbm_mape = fit_and_evaluate(lgbm)
MAPE = 8.78521446433091
In [458]:
svm = SVR(C = 1000, gamma = 0.1)
svm_mape = fit_and_evaluate(svm)
print('Support Vector Machine Regression Performance on the test set: MAE = %0.4f' % svm_mape)
MAPE = 26.660652256377805 Support Vector Machine Regression Performance on the test set: MAE = 26.6607
In [459]:
plt.style.use('fivethirtyeight')
figsize(8, 6)
# Dataframe to hold the results
model_comparison = pd.DataFrame({'model': ['Linear Regression',
'Random Forest', 'Light Gradient Boosted Machine', 'Gradient Boosted Machine',
'K-Nearest Neighbors', 'Support Vector Machine', 'Baseline'],
'mape': [lr_mape, random_forest_mape,
lgbm_mape,gradient_boosted_mape, knn_mape, svm_mape,MAPE_baseline]})
# Horizontal bar chart of test mae
model_comparison.sort_values('mape', ascending = False).plot(x = 'model', y = 'mape', kind = 'barh',
color = 'red', edgecolor = 'black')
# Plot formatting
plt.ylabel(''); plt.yticks(size = 14); plt.xlabel('Mean Absolute Percentage Error'); plt.xticks(size = 14)
plt.title('Model Comparison on validation MAPE', size = 20);
Depending on the run (the exact results change slighty each time), the Gradient Boosting Regressor performs the best followed by Light Gradient Boosting Regressor and the random forrest regressor. I have to admit that this is not the most fair comparison because we are using mostly the default hyperparameters. Especially with the Support Vector Regressor, the hyperparameters have a significant influence on performance. (the random forest and gradient boosting methods are great for starting out because the performance is less dependent on the model settings). I will continue working with gradient boosting regressor (and not random forrest) and optimizing the best model using hyperparamter tuning. Here are the reasons:
- RF (Random Forest) uses decision trees, which are very prone to overfitting. In order to achieve higher accuracy, RF decides to create a large number of them based on bagging. The basic idea is to resample the data over and over and for each sample train a new classifier. Different classifiers overfit the data in a different way, and through voting those differences are averaged out.
- GBM is a boosting method, which builds on weak classifiers. The idea is to add a classifier at a time, so that the next classifier is trained to improve the already trained ensemble ( selection of sample is made more intelligently, subsequently giving more and more weight to hard to classify observations). Notice that for RF each iteration the classifier is trained independently from the rest.
Model Optimization¶
In machine learning, optimizing a model means finding the best set of hyperparameters for a particular problem.
Hyperparameters¶
First, to understand what model hyperparameters are in contrast to model parameters :
- Model hyperparameters are best thought of as settings for a machine learning algorithm that are tuned by the data scientist before training. Examples would be the number of trees in the random forest, or the number of neighbors used in K Nearest Neighbors Regression.
- Model parameters are what the model learns during training, such as the weights in the linear regression.
We control a model by choosing the hyperparameters, and these choices can have a significant effect on the final performance of the model (although usually not as great of an effect as getting more data or engineering features).
Tuning the model hyperparameters controls the balance of under vs over fitting in a model. We can try to correct for under-fitting by making a more complex model, such as using more trees in a random forest. A model that underfits has high bias, and occurs when our model does not have enough capacity (degrees of freedom) to learn the relationship between the features and the target. We can try to correct for overfitting by limiting the complexity of the model and applying regularization. This might mean decreasing the degree of a polynomial regression.. A model that overfits has high variance and in effect has memorized the training set. Both underfitting and overfitting lead to poor generalization performance on the test set.
The problem with choosing the hyperparameters is that no set will work best across all problems. Therefore, for every new dataset, we have to find the best settings. This can be a time-consuming process, but luckily there are several options for performing this procedure in Scikit-Learn. Even better, new libraries, such as TPOT and HyperOpt (Bayesian Hyperparameter Optimization), is aiming to do this process automatically ! For now, I will stick to doing this manually (sort of) in Scikit-Learn!
Hyperparameter Tuning with Random Search and Cross Validation¶
We can choose the best hyperparameters for a model through random search and cross validation.
- Random search refers to the method in which we choose hyperparameters to evaluate: we define a range of options, and then randomly select combinations to try. This is in contrast to grid search which evaluates every single combination we specify. Generally, random search is better when we have limited knowledge of the best model hyperparameters and we can use random search to narrow down the options and then use grid search with a more limited range of options.
- Cross validation is the method used to assess the performance of the hyperparameters. Rather than splitting the training set up into separate training and validation sets which reduces the amount of training data we can use, we use K-Fold Cross Validation. This means dividing the training data into K folds, and then going through an iterative process where we first train on K-1 of the folds and then evaluate performance on the kth fold. We repeat this process K times so eventually we will have tested on every example in the training data with the key that each iteration we are testing on data that we did not train on. At the end of K-fold cross validation, we take the average error on each of the K iterations as the final performance measure and then train the model on all the training data at once. The performance we record is then used to compare different combinations of hyperparameters.
Here I will implement random search with cross validation to select the optimal hyperparameters for the gradient boosting regressor. I will first define a grid then peform an iterative process of: randomly sample a set of hyperparameters from the grid, evaluate the hyperparameters using 4-fold cross-validation, and then select the hyperparameters with the best performance.
In [460]:
# Loss function to be optimized
loss = ['ls']
#loss = ['ls', 'lad', 'huber']
# Number of trees used in the boosting process
n_estimators = [100, 500, 900, 1100, 1500]
# Maximum depth of each tree
max_depth = [2, 3, 5, 10, 15]
# Minimum number of samples per leaf
min_samples_leaf = [1, 2, 4, 6, 8]
# Minimum number of samples to split a node
min_samples_split = [2, 4, 6, 10, 12]
# Maximum number of features to consider for making splits
max_features = ['auto', 'sqrt', 'log2', None]
# Define the grid of hyperparameters to search
hyperparameter_grid = {'loss': loss,
'n_estimators': n_estimators,
'max_depth': max_depth,
'min_samples_leaf': min_samples_leaf,
'min_samples_split': min_samples_split,
'max_features': max_features}
In [461]:
#Split the training set into train and validation set
x_train, x_valid, y_train, y_valid = train_test_split(X, y, test_size=0.2, random_state = 42)
model =GradientBoostingRegressor()
# Set up the random search with 4-fold cross validation
random_cv = RandomizedSearchCV(estimator=model,
param_distributions=hyperparameter_grid,
cv=4, n_iter=25,
scoring = 'neg_mean_absolute_error',
n_jobs = -1, verbose = 1,
return_train_score = True,
random_state=42)
random_cv.fit(x_train, y_train)
Fitting 4 folds for each of 25 candidates, totalling 100 fits
[Parallel(n_jobs=-1)]: Done 42 tasks | elapsed: 14.5s [Parallel(n_jobs=-1)]: Done 100 out of 100 | elapsed: 20.1s finished
Out[461]:
RandomizedSearchCV(cv=4, error_score='raise',
estimator=GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=3, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=1,
min_samples_split=2, min_weight_fraction_leaf=0.0,
n_estimators=100, presort='auto', random_state=None,
subsample=1.0, verbose=0, warm_start=False),
fit_params=None, iid=True, n_iter=25, n_jobs=-1,
param_distributions={'loss': ['ls'], 'n_estimators': [100, 500, 900, 1100, 1500], 'max_depth': [2, 3, 5, 10, 15], 'min_samples_leaf': [1, 2, 4, 6, 8], 'min_samples_split': [2, 4, 6, 10, 12], 'max_features': ['auto', 'sqrt', 'log2', None]},
pre_dispatch='2*n_jobs', random_state=42, refit=True,
return_train_score=True, scoring='neg_mean_absolute_error',
verbose=1)
In [462]:
# Get all of the cv results and sort by the test performance
random_results = pd.DataFrame(random_cv.cv_results_).sort_values('mean_test_score', ascending = False)
random_results.head(3)
Out[462]:
| mean_fit_time | std_fit_time | mean_score_time | std_score_time | param_n_estimators | param_min_samples_split | param_min_samples_leaf | param_max_features | param_max_depth | param_loss | params | split0_test_score | split1_test_score | split2_test_score | split3_test_score | mean_test_score | std_test_score | rank_test_score | split0_train_score | split1_train_score | split2_train_score | split3_train_score | mean_train_score | std_train_score | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 11 | 0.039743 | 0.002046 | 0.0005 | 5.001428e-04 | 100 | 4 | 1 | sqrt | 2 | ls | {'n_estimators': 100, 'min_samples_split': 4, ... | -0.054306 | -0.057804 | -0.084480 | -0.071910 | -0.067125 | 0.011993 | 1 | -0.004404 | -0.004081 | -0.004255 | -0.005858 | -0.004650 | 0.000707 |
| 24 | 0.202966 | 0.005338 | 0.0010 | 4.578320e-07 | 900 | 12 | 8 | sqrt | 3 | ls | {'n_estimators': 900, 'min_samples_split': 12,... | -0.071192 | -0.062028 | -0.074844 | -0.069855 | -0.069480 | 0.004674 | 2 | -0.000178 | -0.000170 | -0.000173 | -0.000200 | -0.000180 | 0.000012 |
| 5 | 0.314700 | 0.003960 | 0.0010 | 3.769729e-07 | 1500 | 10 | 2 | sqrt | 15 | ls | {'n_estimators': 1500, 'min_samples_split': 10... | -0.066434 | -0.053679 | -0.078538 | -0.080963 | -0.069903 | 0.010864 | 3 | -0.000226 | -0.000232 | -0.000217 | -0.000225 | -0.000225 | 0.000005 |
In [463]:
random_cv.best_estimator_
Out[463]:
GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=2,
max_features='sqrt', max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=1, min_samples_split=4,
min_weight_fraction_leaf=0.0, n_estimators=100,
presort='auto', random_state=None, subsample=1.0, verbose=0,
warm_start=False)
The best gradient boosted model has the following hyperparameters:
- loss = ls
- n_estimators = 100
- max_depth = 10
- min_samples_leaf = 4
- min_samples_split = 6
- max_features = 'None'
Using random search is a good method to narrow down the possible hyperparameters to try. Initially, we had no idea which combination would work the best, but this at least narrows down the range of options.
In [464]:
trees_grid = {'n_estimators': [100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800]}
model = GradientBoostingRegressor(loss = 'ls', max_depth = 2,
min_samples_leaf = 4,
min_samples_split = 6,
max_features =None,
n_estimators=100,
random_state = 42)
grid_search = GridSearchCV(estimator = model, param_grid=trees_grid, cv = 4,
scoring = 'neg_mean_absolute_error', verbose = 1,
n_jobs = -1, return_train_score = True)
grid_search.fit(x_train, y_train)
Fitting 4 folds for each of 15 candidates, totalling 60 fits
[Parallel(n_jobs=-1)]: Done 42 tasks | elapsed: 7.7s [Parallel(n_jobs=-1)]: Done 60 out of 60 | elapsed: 10.6s finished
Out[464]:
GridSearchCV(cv=4, error_score='raise',
estimator=GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=4,
min_samples_split=6, min_weight_fraction_leaf=0.0,
n_estimators=100, presort='auto', random_state=42,
subsample=1.0, verbose=0, warm_start=False),
fit_params=None, iid=True, n_jobs=-1,
param_grid={'n_estimators': [100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800]},
pre_dispatch='2*n_jobs', refit=True, return_train_score=True,
scoring='neg_mean_absolute_error', verbose=1)
In [465]:
results = pd.DataFrame(grid_search.cv_results_)
results.head()
Out[465]:
| mean_fit_time | std_fit_time | mean_score_time | std_score_time | param_n_estimators | params | split0_test_score | split1_test_score | split2_test_score | split3_test_score | mean_test_score | std_test_score | rank_test_score | split0_train_score | split1_train_score | split2_train_score | split3_train_score | mean_train_score | std_train_score | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 0.262958 | 0.080836 | 0.000250 | 0.000433 | 100 | {'n_estimators': 100} | -0.078920 | -0.061551 | -0.071311 | -0.078694 | -0.072619 | 0.007085 | 15 | -0.002180 | -0.002165 | -0.001703 | -0.002508 | -0.002139 | 0.000287 |
| 1 | 0.552162 | 0.044587 | 0.001251 | 0.000434 | 150 | {'n_estimators': 150} | -0.078552 | -0.061534 | -0.071282 | -0.078204 | -0.072393 | 0.006907 | 14 | -0.000521 | -0.000492 | -0.000364 | -0.000561 | -0.000485 | 0.000074 |
| 2 | 0.678394 | 0.065337 | 0.001000 | 0.001225 | 200 | {'n_estimators': 200} | -0.078586 | -0.061491 | -0.071260 | -0.078161 | -0.072375 | 0.006924 | 1 | -0.000249 | -0.000255 | -0.000255 | -0.000260 | -0.000255 | 0.000004 |
| 3 | 0.632900 | 0.047653 | 0.000500 | 0.000500 | 250 | {'n_estimators': 250} | -0.078586 | -0.061491 | -0.071260 | -0.078161 | -0.072375 | 0.006924 | 1 | -0.000249 | -0.000255 | -0.000255 | -0.000260 | -0.000255 | 0.000004 |
| 4 | 0.545914 | 0.020159 | 0.000750 | 0.000433 | 300 | {'n_estimators': 300} | -0.078586 | -0.061491 | -0.071260 | -0.078161 | -0.072375 | 0.006924 | 1 | -0.000249 | -0.000255 | -0.000255 | -0.000260 | -0.000255 | 0.000004 |
In [466]:
# Default model
default_model = GradientBoostingRegressor(random_state = 42)
# Select the best model
final_model = grid_search.best_estimator_
final_model
Out[466]:
GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=4,
min_samples_split=6, min_weight_fraction_leaf=0.0,
n_estimators=200, presort='auto', random_state=42,
subsample=1.0, verbose=0, warm_start=False)
In [467]:
%%timeit -n 1 -r 5
default_model.fit(x_train, y_train)
413 ms ± 20 ms per loop (mean ± std. dev. of 5 runs, 1 loop each)
In [468]:
%%timeit -n 1 -r 5
final_model.fit(x_train, y_train)
488 ms ± 41.5 ms per loop (mean ± std. dev. of 5 runs, 1 loop each)
In [469]:
default_pred = default_model.predict(x_valid)
final_pred = final_model.predict(x_valid)
print('Default model performance on the validation set: MAPE = %0.4f.' % mape(y_valid, default_pred))
print('Final model performance on the validation set: MAPE = %0.4f.' % mape(y_valid, final_pred))
Default model performance on the validation set: MAPE = 8.5393. Final model performance on the validation set: MAPE = 7.4867.
The final model does out-perform the baseline model by about 10%, and at the cost of very slightly increased running time. Machine learning is often a field of tradeoffs: bias vs variance, acccuracy vs interpretability, accuracy vs running time, and the final decision of which model to use depends on the situation. Here, the increase in run time is not an impediment; in a different situation, the balance might not be the same so we would need to consider what we are optimizing for and the limitations we have to work with.
To get a sense of the predictions, we can plot the distribution of true values on the validation set and the predicted values on the validation set.
In [470]:
figsize(8, 8)
# Density plot of the final predictions and the test values
sns.kdeplot(final_pred, label = 'Predictions')
sns.kdeplot(y_valid, label = 'Values')
# Label the plot
plt.xlabel('Energy Star Score'); plt.ylabel('Density');
plt.title('Validation Values and Predictions');
C:\Users\Daniela\Anaconda3.5\lib\site-packages\scipy\stats\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result. return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval
The distribution looks to be nearly the same although the density of the predicted values is closer to the median of the validation values rather than to the actual peak at 0.6 and 1.0. It appears the model might be less accurate at predicting the extreme values and instead predicts values closer to the median.
Another diagnostic plot is a histogram of the residuals. Ideally, we would hope that the residuals are normally distributed, meaning that the model is wrong the same amount in both directions (high and low).
In [471]:
figsize = (6, 6)
# Calculate the residuals
residuals = final_pred - y_valid
# Plot the residuals in a histogram
plt.hist(residuals, color = 'red', bins = 20,
edgecolor = 'black')
plt.xlabel('Error'); plt.ylabel('Count')
plt.title('Distribution of Residuals');
The residuals are close to normally disributed, with a few noticeable outliers on the low end. These indicate errors where the model estimate was below that of the true value.
Preparing the testing set and make prediction¶
In [472]:
#save the ids for test set
ids_test = test['week_num']
# Remove the ids and target
X_test = test.drop(columns = ['week_num', 'yield'])
X_test = np.array(X_test)
In [473]:
#make prediction on the test set
preds = final_model.predict(X_test)
In [474]:
# Prepare submission
subm = pd.DataFrame()
subm['week_num'] = ids_test.values
subm['yield'] = preds
subm.to_csv('submission_gbm.csv', index=False)
Feature Importances¶
One of the basic ways we can interpret an ensemble of decision trees is through what are known as the feature importances. These can be interpreted as the variables which are most predictive of the target. While the actual details of the feature importances are quite complex (here is a Stack Overflow question on the subject), we can use the relative values to compare the features and determine which are most relevant to our problem.
In [475]:
train_features = train.drop(columns = ['week_num', 'yield'])
# Extract the feature importances into a dataframe
feature_results = pd.DataFrame({'feature': list(train_features.columns),
'importance': final_model.feature_importances_})
# Show the top 10 most important
feature_results = feature_results.sort_values('importance', ascending = False).reset_index(drop=True)
feature_results.head(10)
Out[475]:
| feature | importance | |
|---|---|---|
| 0 | 4 | 0.047800 |
| 1 | 62 | 0.023703 |
| 2 | 1144 | 0.022820 |
| 3 | 2393 | 0.022171 |
| 4 | 2297 | 0.020770 |
| 5 | 2226 | 0.019661 |
| 6 | 2267 | 0.018839 |
| 7 | 2 | 0.016693 |
| 8 | 2179 | 0.016467 |
| 9 | 2241 | 0.015411 |
We could use feature importance to perform feature selection; however, this is not an important process when using boosting trees algorithm as is for a linear model as linear regression. It might bring the actual model to perform even poorer.
I will extract the most 10 important features and train both a linear regression and a boosting tree algorithm and compare their performance.
In [476]:
# Extract the names of the most important features
most_important_features = feature_results['feature'][:10]
# Find the index that corresponds to each feature name
indices = [list(train.columns).index(x) for x in most_important_features]
# Keep only the most important features
x_train_reduced = x_train[:, indices]
x_valid_reduced = x_valid[:, indices]
print('Most important training features shape: ', x_train_reduced.shape)
print('Most important validation features shape: ', x_valid_reduced.shape)
Most important training features shape: (92, 10) Most important validation features shape: (23, 10)
In [477]:
lr = LinearRegression()
# Fit on full set of features
lr.fit(x_train, y_train)
lr_full_pred = lr.predict(x_valid)
# Fit on reduced set of features
lr.fit(x_train_reduced, y_train)
lr_reduced_pred = lr.predict(x_valid_reduced)
# Display results
print('Linear Regression Full Results: MAE = %0.4f.' % mape(y_valid, lr_full_pred))
print('Linear Regression Reduced Results: MAE = %0.4f.' % mape(y_valid, lr_reduced_pred))
Linear Regression Full Results: MAE = 16.1531. Linear Regression Reduced Results: MAE = 15.2784.
Well, reducing the features did improve the linear regression results! It turns out that eliminating the features with low importance do actually improve performance in case of linear regression.
In [478]:
# Create the model with the same hyperparamters
model_reduced = GradientBoostingRegressor(alpha=0.9, criterion='friedman_mse', init=None,
learning_rate=0.1, loss='ls', max_depth=2, max_features=None,
max_leaf_nodes=None, min_impurity_decrease=0.0,
min_impurity_split=None, min_samples_leaf=4,
min_samples_split=6, min_weight_fraction_leaf=0.0,
n_estimators=200, presort='auto', random_state=42,
subsample=1.0, verbose=0, warm_start=False)
# Fit and test on the reduced set of features
model_reduced.fit(x_train_reduced, y_train)
model_reduced_pred = model_reduced.predict(x_valid_reduced)
print('Gradient Boosted Reduced Results: MAE = %0.4f' % mape(y_valid, model_reduced_pred))
Gradient Boosted Reduced Results: MAE = 15.7505
It seems that it does not happen the same thing for the gradient boosting algorithm, where the extra information in the features with low importance improve performance.
Locally Interpretable Model-agnostic Explanations¶
I will use LIME to explain individual predictions made by the model. LIME is aimed at showing how a machine learning model thinks by approximating the region around a prediction with a linear model.
I will look at trying to explain the predictions on an example the model gets very wrong and an example the model gets correct(well, slmodt correct!). I will restrict to using the reduced set of 10 features to aid interpretability. The model trained on the 10 most important features is much less accurate, but we generally have to trade off accuracy for interpretability!
In [479]:
# Find the residuals
y_valid= np.array(y_valid)
residuals = abs(model_reduced_pred - y_valid)
# Exact the worst and best prediction
wrong = x_valid_reduced[np.argmax(residuals), :]
right = x_valid_reduced[np.argmin(residuals), :]
In [480]:
# Create a lime explainer object
explainer = lime.lime_tabular.LimeTabularExplainer(training_data = x_train_reduced,
mode = 'regression',
training_labels = y_train,
feature_names = list(most_important_features))
In [481]:
# Display the predicted and true value for the wrong instance
print('Prediction: %0.4f' % model_reduced.predict(wrong.reshape(1, -1)))
print('Actual Value: %0.4f' % y_valid[np.argmax(residuals)])
# Explanation for wrong prediction
wrong_exp = explainer.explain_instance(data_row = wrong,
predict_fn = model_reduced.predict)
# Plot the prediction explaination
wrong_exp.as_pyplot_figure();
plt.title('Explanation of Prediction', size = 28);
plt.xlabel('Effect on Prediction', size = 22);
Prediction: 0.8343 Actual Value: 0.5700
In [483]:
wrong_exp.show_in_notebook(show_predicted_value=False)
In this example, our gradient boosted model predicted a yield of 0.8343 and the actual value was 0.57.
The plot from LIME is showing us the contribution to the final prediction from each of the features for the example. We can see that variable 2 increased the prediction because it was under 0.68. The variable 2241 on the other hand, dicreased the prediction because it was equal tp 0.17.
We can interpret this as saying that our model thought the yield would be much higher than it actually was because the variable 4 was high. However, in this case, the yield was 0.57 despite the high value of the variable 4. While this significant mistake (off by 0.264!) might initially have been confusing, now we can see that in reality, the model was reasoning through the problem and just arrived at the incorrect value! A human going over the same process probably would have arrived at the same conclusion (if they had the patience to go through all the data).
Now we can go through the same process with a prediction the model got correct.
In [484]:
print('Prediction: %0.4f' % model_reduced.predict(right.reshape(1, -1)))
print('Actual Value: %0.4f' % y_valid[np.argmin(residuals)])
# Explanation for wrong prediction
right_exp = explainer.explain_instance(right, model_reduced.predict, num_features=10)
right_exp.as_pyplot_figure();
plt.title('Explanation of Prediction', size = 28);
plt.xlabel('Effect on Prediction', size = 22);
Prediction: 0.6194 Actual Value: 0.6200
In [485]:
right_exp.show_in_notebook(show_predicted_value=False)
The correct value for this case was 0.6194 which our gradient boosted model got almost right with 0.62 !
The plot from LIME again shows the contribution to the prediciton of each of feature variables for the example. For instance, because the variable 2 was more than -0.04, that contributed slightly significant to a higher estimate of the yield. Likewise, the variable 4 being equal to -0.08 also negatively contributed to the final prediction.
Observing break down plots like these allow us to get an idea of how the model makes a prediction. This is probably most valuable for cases where the model is off by a large amount as we can inspect the errors and perhaps engineer better features or adjust the hyperparameters of the model to improve predictions for next time. The examples where the model is off the most could also be interesting edge cases to look at manually.
Examining a Single Decision Tree¶
One of the best part about a tree-based ensemble is that we can look at any individual estimator. Although the final model is composed of 200 decision trees, and looking at a single one is not indicative of the entire model, it still allows us to see the general idea of how a decision tree works. From there, it is a natural extension to imagine hundreds of these trees building off the mistakes of previous trees to make a final prediction (this is a significant oversimplification of how gradient boosting regression works!)
I will first extract a tree from the forest and then save it using sklearn.tree.export_graphviz. This saves the tree as a .dot file which can be converted to a png using command line instructions Anaconda terminal.
In [486]:
# Extract a single tree
import pydotplus
single_tree = model_reduced.estimators_[105][0]
export_graphviz(single_tree, out_file = 'images/tree.dot',
rounded = True,
feature_names = most_important_features,
filled = True)
single_tree
Out[486]:
DecisionTreeRegressor(criterion='friedman_mse', max_depth=2,
max_features=None, max_leaf_nodes=None,
min_impurity_decrease=0.0, min_impurity_split=None,
min_samples_leaf=4, min_samples_split=6,
min_weight_fraction_leaf=0.0, presort='auto',
random_state=<mtrand.RandomState object at 0x00000288A70889D8>,
splitter='best')
In [103]:
# Convert to a png from the command line
# This requires the graphviz visualization library (https://www.graphviz.org/)
#from command line transform from .dot tp .png
# dot -Tpng images/tree.dot -o images/tree.png
Now we can take a look at the tree and try to intrepret it's decisions! The best way to think of a decision tree is as a series of yes/no questions, like a flowchart. We start at the top, called the root, and move our way down the tree, with the direction of travel determined by the answer to each equation.
For instance, here the first question we ask is: is the variable 2257 less than or equal to -0.031? If the answer is yes, then we move to the left and ask the question: is the variable 2257 less than or equal to -0.061? If the answer to the first question was no, we move to the right and ask the question is the variable 169 less than or equal to -0.176?
We continue this iterative process until we reach the bottom of the tree and end up in a leaf node. Here, the value we predict corresponds to the value shown in the node (the values in this tree appear to be the actual predictions divided by 100).
Each node has four different pieces of information:
The question: based on this answer we move right or left to the next node a layer down in the tree The friedman_mse: a measure of the error for all of the examples in a given node The samples: number of examples in a node The value: the prediction of the target for all examples in a node
Conclusion¶
This is a small tree, where the model estimates the same value for each example in a node; however there is not a larger error because (this is my guessing) all of the examples have the same target value. However, with a bigger tree depth, the model would have a greater error.
In this case, and also to answer the question "What will make this problem set easier to solve?", the algorithm would most probably do better with a larger data set (i.e. imput from more weeks), and could also grow in depth (not too large, as too large tree algorithms can lead to overfitting).
As an alternative model, I would use a Bayesian regression model, for which I would use Markov Chain Monte Carlo and the data to find most likely parameters for the selected posterior distribution, and further use the posterior probability as the prior for applying Bayes Rule using additional hypothetical weather conditions data. I would set this model to give me interval predictions, as this is more correctly than just a single value.